In this section, you will learn to: identify unit graphs of various functions transform a unit graph...
-
Upload
elisabeth-stokes -
Category
Documents
-
view
214 -
download
0
Transcript of In this section, you will learn to: identify unit graphs of various functions transform a unit graph...
![Page 1: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/1.jpg)
![Page 2: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/2.jpg)
In this section, you will learn to:identify unit graphs of various
functionstransform a unit graph by
stretching, shifting and reflectingwrite the equation of a transformed
graph using the sketch of the graph
![Page 3: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/3.jpg)
Common Unit Graphs:1) Constant Function:
3f x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
x
y
3f x
1 2 3 4 5-1-2-3-4-5
1
2
-1
-2
-3
-4
-5
x
y
![Page 4: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/4.jpg)
Common Unit Graphs:2) Linear Function:
f x x
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
![Page 5: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/5.jpg)
Common Unit Graphs:3) Absolute Value Function:
f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
x
y
![Page 6: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/6.jpg)
Common Unit Graphs:3) Absolute Value Function:
f x x
1 2 3 4-1-2-3-4
1
2
3
4
-1
x
y
![Page 7: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/7.jpg)
Common Unit Graphs:4) Quadratic Function:
2f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
x
y
![Page 8: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/8.jpg)
Common Unit Graphs:4) Quadratic Function:
2f x x
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
x
y
![Page 9: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/9.jpg)
Common Unit Graphs:5) Square Root Function:
f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
x
y
![Page 10: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/10.jpg)
Common Unit Graphs:5) Square Root Function:
f x x
1 2 3 4-1-2
1
2
3
4
-1
-2
x
y
![Page 11: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/11.jpg)
Common Unit Graphs:6) Cubic Function:
3f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
![Page 12: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/12.jpg)
Common Unit Graphs:6) Cubic Function:
3f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
![Page 13: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/13.jpg)
Common Unit Graphs:7) Rational Function:
1f x
x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
![Page 14: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/14.jpg)
Common Unit Graphs:7) Rational Function:
1f x
x
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
-3
-4
x
y
![Page 15: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/15.jpg)
Summary of Graphing:Rigid Transformations: Shape/size do not
change a) Vertical shift c units upward: h x f x c
2f x x 2 2f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1 2 3-1-2-3
1
2
3
4
5
6
-1
x
y
![Page 16: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/16.jpg)
Summary of Graphing:Rigid Transformations: b) Vertical shift c units downward:
h x f x c
2f x x 2 2f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1 2 3-1-2-3
1
2
-1
-2
-3
x
y
![Page 17: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/17.jpg)
Summary of Graphing:Rigid Transformations: c) Horizontal shift c units to the
right: h x f x c
2f x x 22f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1 2 3 4 5-1
1
2
3
4
-1
x
y
![Page 18: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/18.jpg)
Summary of Graphing:Rigid Transformations: d) Horizontal shift c units to the left:
h x f x c
2f x x 22f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1-1-2-3-4-5
1
2
3
4
-1
x
y
![Page 19: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/19.jpg)
Summary of Graphing:Rigid Transformations: e) Reflection across the x-axis:
h x f x
2f x x 2f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1 2 3-1-2-3
1
-1
-2
-3
-4
-5
x
y
![Page 20: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/20.jpg)
Summary of Graphing:Rigid Transformations: f) Reflection across the y-axis:
f x x f x x
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
x
y
1 2 3 4-1-2-3-4
1
2
3
4
-1
-2
x
y
h x f x
![Page 21: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/21.jpg)
Summary of Graphing:Non-Rigid Transformations:
Shape/size will change a) Vertical stretch by c units if c >
1 : h x c f x 2f x x 22f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1 2 3-1-2-3
1
2
3
4
-1
x
y
![Page 22: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/22.jpg)
Summary of Graphing:Non-Rigid Transformations: b) Vertical shrink by c units if 0 < c <
1: h x c f x
2f x x 21
2f x x
1 2 3-1-2-3
1
2
3
4
-1
x
y
1 2 3-1-2-3
1
2
3
4
-1
x
y
![Page 23: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/23.jpg)
Graphing Examples:Describe the transformation of the
followingFunction:
This is an absolute value function shifteda) 4 units to the rightb) 6 units upc) reflection across the x-axisd) vertical shrink
14 6
2f x x
![Page 24: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/24.jpg)
Graphing Examples:
14 6
2f x x f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
x
y
2 4 6 8 10 12-2-4
1
2
3
4
5
6
-1
-2
x
y
![Page 25: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/25.jpg)
Y-Axis Reflection Graphing Examples:
2 4 1f x x f x x
2 4 1f x x
1 2 3 4 5 6-1-2-3-4
1
2
-1
-2
-3
-4
-5
-6
x
y
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
![Page 26: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/26.jpg)
Graphing Examples:Write a cubic equation with the
followingtransformations:
a) 3 units to the leftb) 2 units downc) reflection across the x-axisd) vertical stretch 33 3 2f x x
![Page 27: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/27.jpg)
Graphing Examples:
33 3 2f x x 3f x x
1 2 3 4 5-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
1 2-1-2-3-4-5
1
2
3
4
5
-1
-2
-3
-4
-5
x
y
![Page 28: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/28.jpg)
Writing an Equation: Write the equation of the graph
below.
1 2 3 4 5 6 7 8 9 10-1
1
2
3
4
-1
-2
-3
-4
x
y
![Page 29: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/29.jpg)
Writing an Equation: Write the equation of the graph
below.
f x x
1 2 3 4 5 6 7 8 9 10-1
1
2
3
4
-1
-2
-3
-4
x
y
![Page 30: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/30.jpg)
Writing an Equation: Write down the transformations.
3 units right 2 units up x-axis reflection Use (4,1) as a point on the graph
1 4 3 2
1 2
1 3 2
y a x h k
a
a
a y x
![Page 31: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/31.jpg)
Writing an Equation: Write the quadratic equation of the
graph below.
1 2 3 4 5 6 7-1-2-3-4-5
1
2
3
-1
-2
-3
-4
-5
x
y
![Page 32: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/32.jpg)
Writing an Equation: The vertex has been translated 1
unit to the right and 1 unit up. This represents (h,k).
The graph has been reflected across the x-axis.
Use one point on the graph, the vertex and solve for the value of a for the quadratic equation
2 .y a x h k
![Page 33: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/33.jpg)
Writing an Equation: The vertex is (h,k) which is (1,1). One point on the graph is Solve for a.
2
21 3 1 1
2 4
1
2
y a x h k
a
a
a
3, 1 .
21Therefore, 1 1
2y x
![Page 34: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/34.jpg)
Writing an Equation: Sketch the graph given the
following function.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
![Page 35: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/35.jpg)
Writing an Equation: Sketch the graph of f(x+1) given
the following function.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
![Page 36: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/36.jpg)
Writing an Equation: Sketch the graph of f(x)-3 given the
following function.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
![Page 37: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/37.jpg)
Writing an Equation: Sketch the graph of f(-x) given the
following function.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
![Page 38: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/38.jpg)
Writing an Equation: Sketch the graph of - f(x)+1 given the
following function.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y
![Page 39: In this section, you will learn to: identify unit graphs of various functions transform a unit graph by stretching, shifting and reflecting write the.](https://reader030.fdocuments.net/reader030/viewer/2022020417/5697bff81a28abf838cbf20f/html5/thumbnails/39.jpg)
Writing an Equation: Sketch the graph of 2f(x)-1 given the
following function.
1 2 3 4 5 6-1-2-3-4-5-6
1
2
3
4
5
6
-1
-2
-3
-4
-5
-6
x
y