FUNCTIONS AND ABSOLUTE VALUE

Unit One Test Review

FOR THE TEST, I NEED TO KNOW HOW TO…

Find the domain and range of a function given its graph

Perform operations on functions (add, subtract, multiply, divide)

Compose two functions

Find and verify inverses

Graph absolute value functions

Solve absolute value equations and inequalities

DOMAIN AND RANGE

FIND THE DOMAIN

-1 1 2 3 4 5 6 7 8

-5

-4

-3

-2

-1

1

2

3

x

y

FIND THE DOMAIN

-3 -2 -1 1 2 3 4 5 6

-6

-5

-4

-3

-2

-1

1

2

x

y

FIND THE DOMAIN

-5 -4 -3 -2 -1 1 2 3 4

-7

-6

-5

-4

-3

-2

-1

1

x

y

FIND THE DOMAIN AND RANGE

-7 -6 -5 -4 -3 -2 -1 1

-5

-4

-3

-2

-1

1

2

3

x

y

FIND THE DOMAIN AND RANGE

-3 -2 -1 1 2 3 4 5 6

-3

-2

-1

1

2

3

4

5

x

y

FUNCTION OPERATIONS

F(X) = 3X – 5 G(X) = -2X + 1

Find f(x) – g(x)

F(X) =X²+ 1 G(X) = X – 5

Find f(g(x))

F(X) = 3X – 5 G(X) = -2X + 1

Find g(f(-3))

F(X) = 3X – 5 G(X) = -2X + 1

Find f(x) g(x)

F(X) =X²+ 1 G(X) = X – 5

Find g(f(x))

INVERSE FUNCTIONS

VERIFY THAT THE TWO FUNCTIONS ARE INVERSES

F(x) = 0.5x + 4F -1(x) = 2x – 8

FIND THE INVERSE FUNCTION

y = x2 + 4

FIND THE INVERSE FUNCTION

y = 3x +7

FIND THE INVERSE FUNCTION

y = -2x + 6

GRAPHING ABSOLUTE VALUE

FIND THE VERTEX POINT

y = -2|x – 4| + 5

FIND THE VERTEX POINT

y = 3|2x + 6| - 1

DESCRIBE THE TRANSFORMATIONS

y = -|x + 3| - 8

GRAPH THE FUNCTION

y = 2|x + 4| - 7

GRAPH THE FUNCTION

y = -|x – 1| + 5

SOLVING ABSOLUTE VALUE

SOLVE THE EQUATION

7 = 2|x – 3| + 1

SOLVE THE EQUATION

4x + 3 = |2x – 3|

GRAPH THE SOLUTION TO THE INEQUALITY

2|x – 6| < 20

GRAPH THE SOLUTION TO THE INEQUALITY

|2x – 8| > x + 5