1.3 Families of Equations. What families of graphs have your studied? Linear Absolute Value...

1.3 Families of Equations

What families of graphs have your studied?

•Linear

•Absolute Value

•Quadratic •Square Root •Cubic•Cube Root

How do you recognize the various families?

Linear Family

Equation:

Graph:

y = mx + bAx + By + C = 0 Line: m = +

m = –m = 0

Examples:Graph the following linear equations:

y = 3x - 5

Domain--

Range--

Increasing/Decreasing?

Odd/Even

Examples:Graph the following linear equations:

2x – 3y = 12

Domain--

Range--


Odd or Even?


Absolute Value Family

Equation:

Graph:

y = a|x – h| + k

(h,k)

(h,k)

a = – a = +

Examples:Graph the following absolute value equations:

y = |x|

Domain--

Range--


Odd or Even?


y = |x - 2|+ 3

Domain--

Range--


Odd or Even


y = |x + 6|+ 5

Domain--

Range--


Odd or Even


y = -|x - 1|-3

Domain--

Range--


Odd or Even?


Quadratic Family

Equation:

Graph:

Pattern:

y = a(x – h)2 + ky = ax2 + bx + c

a = –(h,k)

a = +

(h,k)

1, 3, 5

Examples:Graph the following quadratic equations:

y = x2

Domain--

Range--


Odd or Even


y = (x-1)2

Domain--

Range--


Odd or Even?


y = -(x-2)2 + 4

Domain--

Range--

Increasing/Decreasing

Odd or Even?


y = x2 + 4x - 1

Hint: x = -b 2a


Square Root Family

Equation:

Graph:

Pattern:

a = – a = +

y = a√x – h + k

(h,k)

or (h,k)

or

1, 3, 5

y = a(x – h)1/2 + k

Examples:Graph the following square root equations:

y = √x

Domain--

Range--


Examples:

y = √x – 3 + 2

Graph the following square root equations:

Domain--

Range--



Cubic Family

Equation:

Graph:

Pattern:

y = a(x – h)3 + k

a = –(h,k)

a = +

(h,k)

1, 7

Examples:Graph the following cubic equations:

y = x3

Domain--

Range--



y = x3 - 1

Domain--

Range--



y = -(x-2)3 + 4

Domain--

Range--



Cube Root Family

Equation:

Graph:

Pattern:

a = – a = +

y = a 3√x – h + k

(h,k) (h,k)

1, 7

y = a(x – h)1/3 + k

Examples:

y = 3√x

Graph the following cube root equations:

Domain--

Range--


Examples:

y = 3√x – 3 + 2

Graph the following cube root equations:

Domain--

Range--


Identify the family of graphs for the following equations:

Equation Family3x + 2y = 6

y = (x – 2)2 + 1

y = | x – 4 | + 6

y = 3x2 + 6x – 2

y = 2 x – 1 + 4

y = – 3 4 – x + 2

(x – 2)2 + (y – 6) 2 = 4


Equation Familyy = 2/3 | x – 4 | + 1

y = 1 – x

x = 5

x2 +y2 + 3x -1 = 0

x2 + y2 = 84

y = – 3 x + 1 – 3

y = – 2


Equation Familyy = – ( x – 4 ) 2

y = 2x2 + 1

y = 3/2 x – 2

y = –2 | x |

y = (x – 8)1/3 - 3

Average Rate of Change

f(x2) – f(x1) x2 - x1

Change in yChange in x

msec

A function y = f(x) is even iff(-x) = f(x)

A function y = f(x) is odd iff(-x) = -f(x)

1.3 Families of Equations. What families of graphs have your studied? Linear Absolute Value...

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