11 x1 t02 06 relations & functions (2013)
-
Upload
nigel-simmons -
Category
Education
-
view
273 -
download
2
Transcript of 11 x1 t02 06 relations & functions (2013)
![Page 1: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/1.jpg)
Relations & Functions
![Page 2: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/2.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
![Page 3: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/3.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
![Page 4: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/4.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
![Page 5: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/5.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
![Page 6: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/6.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
![Page 7: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/7.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
function
![Page 8: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/8.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
function
y
x
2x y
![Page 9: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/9.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
function
y
x
2x y
![Page 10: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/10.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
function
y
x
2x y
function
![Page 11: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/11.jpg)
Relations & Functions2 2e.g. 25x y
A relation is a set of any ordered pairs that are related in any way.
2e.g. y x
A function is a relation such that for any x value, there is a maximum of one y value.
Straight Line TestIf a straight line is drawn parallel to the y axis, it will only cross a function once, if at all.
y
x
1yx
function
y
x
2x y
function
note: actually two functions
and y x y x
![Page 12: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/12.jpg)
Domain and Range y f x
![Page 13: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/13.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.
![Page 14: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/14.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.“Domain is the INPUT of the function/relation”
![Page 15: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/15.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.
To find a domain, look for values x could not be.
“Domain is the INPUT of the function/relation”
![Page 16: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/16.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.
To find a domain, look for values x could not be.e.g.
y
x
2x y
“Domain is the INPUT of the function/relation”
![Page 17: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/17.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.
To find a domain, look for values x could not be.e.g.
y
x
2x y
domain: 0x
“Domain is the INPUT of the function/relation”
![Page 18: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/18.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.
To find a domain, look for values x could not be.e.g.
y
x
2x y
domain: 0x
y
x213
y f x
“Domain is the INPUT of the function/relation”
![Page 19: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/19.jpg)
Domain and Range y f x
Domain: All possible values of x that can be substituted into the function/relation.
To find a domain, look for values x could not be.e.g.
y
x
2x y
domain: 0x
y
x213
y f x
domain: 0 and 2x x
“Domain is the INPUT of the function/relation”
![Page 20: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/20.jpg)
Things to look for:
1. Fractions:
![Page 21: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/21.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
![Page 22: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/22.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
![Page 23: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/23.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x
![Page 24: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/24.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
![Page 25: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/25.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
![Page 26: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/26.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
2 1 0x
2 11
xx
![Page 27: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/27.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
2 1 0x
domain: all real except 1x x
2 11
xx
![Page 28: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/28.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
2 1 0x
domain: all real except 1x x
2 11
xx
4 3 1 7
xiii yx x
![Page 29: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/29.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
2 1 0x
domain: all real except 1x x
2 11
xx
4 3 1 7
xiii yx x
1 0x
1x
![Page 30: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/30.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
2 1 0x
domain: all real except 1x x
2 11
xx
4 3 1 7
xiii yx x
1 0x
1x
7 0x
7x
![Page 31: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/31.jpg)
Things to look for:
1. Fractions: bottom of fraction 0
1e.g. i yx
0x domain: all real except 0x x
21
1ii y
x
2 1 0x
domain: all real except 1x x
2 11
xx
4 3 1 7
xiii yx x
1 0x
domain: all real except 1 or 7x x
1x
7 0x
7x
![Page 32: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/32.jpg)
2. Root Signs:
![Page 33: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/33.jpg)
2. Root Signs: you can’t find the square root of a negative number.
![Page 34: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/34.jpg)
2. Root Signs:
2e.g. 4i y x
you can’t find the square root of a negative number.
![Page 35: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/35.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
you can’t find the square root of a negative number.
2 4x
![Page 36: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/36.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 37: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/37.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 38: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/38.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
3 03
xx
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 39: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/39.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
3 03
xx
5 05
xx
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 40: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/40.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
3 03
xx
domain: 3 5x
5 05
xx
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 41: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/41.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
3 03
xx
domain: 3 5x
5 05
xx
1 2
iii yx
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 42: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/42.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
3 03
xx
domain: 3 5x
5 05
xx
1 2
iii yx
2 0x
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 43: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/43.jpg)
2. Root Signs:
2e.g. 4i y x 24 0x
3 5ii y x x
3 03
xx
domain: 3 5x
5 05
xx
1 2
iii yx
2 0x domain: 2x
you can’t find the square root of a negative number.
2 4x domain: 2 2x
![Page 44: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/44.jpg)
Range: All possible y values obtained by substituting in the domain
![Page 45: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/45.jpg)
Range: All possible y values obtained by substituting in the domain“Range is the OUTPUT of the function/relation”
![Page 46: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/46.jpg)
Range: All possible y values obtained by substituting in the domain
e.g.y
x
2x y
“Range is the OUTPUT of the function/relation”
![Page 47: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/47.jpg)
Range: All possible y values obtained by substituting in the domain
e.g.y
x
2x y
range: all real y
“Range is the OUTPUT of the function/relation”
![Page 48: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/48.jpg)
Range: All possible y values obtained by substituting in the domain
e.g.y
x
2x y
range: all real y
y
x213
y f x
“Range is the OUTPUT of the function/relation”
![Page 49: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/49.jpg)
Range: All possible y values obtained by substituting in the domain
e.g.y
x
2x y
range: all real y
y
x213
y f x
range: 1 and 3y y
“Range is the OUTPUT of the function/relation”
![Page 50: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/50.jpg)
Things to look for:
1. Maximum/Minimum values:
![Page 51: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/51.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
![Page 52: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/52.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y x
![Page 53: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/53.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
![Page 54: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/54.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x
![Page 55: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/55.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
![Page 56: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/56.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
![Page 57: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/57.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
![Page 58: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/58.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y
![Page 59: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/59.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y range: 5y
![Page 60: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/60.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y range: 5y
2iv y x
![Page 61: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/61.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y range: 5y
2iv y x range: 0y
![Page 62: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/62.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y range: 5y
2iv y x range: 0y
2 5v y x
![Page 63: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/63.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y range: 5y
2iv y x range: 0y
2 5v y x 0 5y
![Page 64: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/64.jpg)
Things to look for:
1. Maximum/Minimum values: even powers and absolute valuesare always 0
2e.g. i y xrange: 0y
2 3ii y x 0 3y
range: 3y
2 5iii y x
5 0y range: 5y
2iv y x range: 0y
2 5v y x 0 5y
range: 5y
![Page 65: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/65.jpg)
2. Restrictions on Domain:
![Page 66: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/66.jpg)
2. Restrictions on Domain: sub in endpoints and centre of domain
![Page 67: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/67.jpg)
2. Restrictions on Domain:2e.g. 4y x
sub in endpoints and centre of domain
![Page 68: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/68.jpg)
2. Restrictions on Domain:2e.g. 4y x
sub in endpoints and centre of domain
domain: 2 2x
![Page 69: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/69.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
sub in endpoints and centre of domain
domain: 2 2x
![Page 70: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/70.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
sub in endpoints and centre of domain
domain: 2 2x
![Page 71: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/71.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
sub in endpoints and centre of domain
domain: 2 2x
![Page 72: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/72.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
![Page 73: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/73.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
![Page 74: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/74.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
![Page 75: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/75.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y
![Page 76: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/76.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
![Page 77: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/77.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
![Page 78: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/78.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y
![Page 79: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/79.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y range: all real except 5y y
![Page 80: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/80.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y range: all real except 5y y
7 4
xiii yx
![Page 81: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/81.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y range: all real except 5y y
7 4
xiii yx
4 7x x
4x
1
3
![Page 82: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/82.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y range: all real except 5y y
7 4
xiii yx
314
yx
4 7x x 4x
1
3
![Page 83: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/83.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y range: all real except 5y y
7 4
xiii yx
314
yx
4 7x x 4x
1
3
1 0y
![Page 84: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/84.jpg)
2. Restrictions on Domain:2e.g. 4y x 2when 2, 4 2
0x y
2when 0, 4 0 2
x y
range: 0 2y
If you have a constant on the top of the fraction, fraction 0
sub in endpoints and centre of domain
domain: 2 2x
3. Fractions:
1e.g. i yx
0y range: all real except 0y y
1 5ii yx
5 0y range: all real except 5y y
7 4
xiii yx
314
yx
4 7x x 4x
1
3
1 0y
range: all real except 1y y
![Page 85: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/85.jpg)
Function Notation
![Page 86: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/86.jpg)
Function Notation
2e.g. 3 4f x x
![Page 87: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/87.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
![Page 88: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/88.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
23 5 4
![Page 89: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/89.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4
![Page 90: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/90.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4 ) b f a
![Page 91: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/91.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4 ) b f a 23 4a
![Page 92: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/92.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4 ) b f a 23 4a
) c f x h f x
![Page 93: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/93.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4 ) b f a 23 4a
2 23 4 3 4x h x ) c f x h f x
![Page 94: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/94.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4 ) b f a 23 4a
2 23 4 3 4x h x ) c f x h f x 2 2 23 6 3 4 3 4x xh h x
26 3xh h
![Page 95: 11 x1 t02 06 relations & functions (2013)](https://reader033.fdocuments.net/reader033/viewer/2022052400/559c345e1a28ab5e5d8b48a7/html5/thumbnails/95.jpg)
) 5a f
Function Notation
2e.g. 3 4f x x
75 479
23 5 4 ) b f a 23 4a
2 23 4 3 4x h x ) c f x h f x 2 2 23 6 3 4 3 4x xh h x
Exercise 2F; 1, 2, 3acdfi, 4begh, 5a, 6, 7a, 8abd,10abdf, 11aceh, 12bd, 14*
26 3xh h