Exploring Composition of Functions and Equations

What is the primary goal when finding compositions of functions using graphs and tables?

• To find the x-value given a y-value

• To determine the domain of the function

• To find the y-value given an x-value

• To find the slope of the graph

If f(x) = -3x - 9, what is f(f(-3))?

• 9

• -18

• -9

• 0

Given f(x) = -3x - 9 and g(x) = x + 8, what is g(f(2))?

• 23

• 31

• -7

• 15

If f(x) = -3x + 1, what is f(f(-3))?

• 10

• 44

• -10

• 0

What is the result of g(g(-6)) if g(x) = 5x - 6?

• -36

• 30

• -186

• -180

What is f(f(x)) if f(x) = -3x - 9?

• -9x - 18

• 3x + 9

• 9x + 18

• -3x - 9

What is g(f(x)) if f(x) = -3x - 9 and g(x) = x + 8?

• -3x + 17

• 3x + 17

• -3x - 1

• 3x + 9

What is f(g(x)) if f(x) = -3x + 1 and g(x) = 5x - 6?

• 15x + 19

• -15x - 19

• 15x - 19

• -15x + 19

What is g(f(x)) if f(x) = -3x + 1 and g(x) = 5x - 6?

• 15x + 1

• -15x - 1

• 15x - 1

• -15x + 1

What is the simplified form of f(g(x)) if f(x) = -3x + 1 and g(x) = 5x - 6?

• -15x - 1

• 15x + 1

• -15x + 1

• 15x - 1