F UNCTIONS AND A BSOLUTE V ALUE Unit One Test Review

F OR 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

D OMAIN AND R ANGE

F IND THE DOMAIN

F IND THE DOMAIN AND RANGE

F UNCTION O PERATIONS

F ( X ) = 3 X – 5 G ( X ) = -2 X + 1  Find f(x) – g(x)

F ( X ) = X ²+ 1 G ( X ) = X – 5  Find f(g(x))

F ( X ) = 3 X – 5 G ( X ) = -2 X + 1  Find g(f(-3))

F ( X ) = 3 X – 5 G ( X ) = -2 X + 1  Find f(x) g(x)

F ( X ) = X ²+ 1 G ( X ) = X – 5  Find g(f(x))

I NVERSE F UNCTIONS

V ERIFY THAT THE TWO FUNCTIONS ARE INVERSES F(x) = 0.5x + 4 F -1 (x) = 2x – 8

F IND THE INVERSE F UNCTION y = x 2 + 4

F IND THE INVERSE F UNCTION y = 3x +7

F IND THE INVERSE F UNCTION y = -2x + 6

G RAPHING A BSOLUTE V ALUE

F IND THE V ERTEX P OINT y = -2|x – 4| + 5

F IND THE V ERTEX P OINT y = 3|2x + 6| - 1

D ESCRIBE THE T RANSFORMATIONS y = -|x + 3| - 8

G RAPH THE FUNCTION y = 2|x + 4| - 7

G RAPH THE F UNCTION y = -|x – 1| + 5

S OLVING A BSOLUTE V ALUE

S OLVE THE EQUATION 7 = 2|x – 3| + 1

S OLVE THE EQUATION 4x + 3 = |2x – 3|

G RAPH THE SOLUTION TO THE INEQUALITY 2|x – 6| < 20

G RAPH THE SOLUTION TO THE I NEQUALITY |2x – 8| > x + 5