Composite Functions and Evaluations

The video tutorial introduces composite functions, explaining how to evaluate them using graphs. It demonstrates the process with examples, such as evaluating g(f(-4)), g(f(7)), and g(f(-6)), by finding corresponding y-values on given graphs. The tutorial emphasizes understanding the path of functions and finding y-values without relying on graphs in future lessons.

What is a composite function?

• A function that is applied to the result of another function

• A function that is multiplied by another function

• A function that is added to another function

• A function that is divided by another function

In the expression g(f(-4)), what is the first step?

• Find the value of g at x = -4

• Find the value of g at x = 4

• Find the value of f at x = -4

• Find the value of f at x = 4

What is the y-value of f when x = -4?

• 1

• -1

• 0

• 4

After finding f(-4) = -1, what is the next step in evaluating g(f(-4))?

• Find f(1)

• Find g(-1)

• Find g(1)

• Find f(-1)

What is the final value of g(f(-4))?

• -3

• 3

• 0

• 1

In the expression g(f(7)), what is the first step?

• Find the value of g at x = -7

• Find the value of g at x = 7

• Find the value of f at x = 7

• Find the value of f at x = -7

What is the y-value of f when x = 7?

• 3

• 7

• -3

• 0

After finding f(7) = -3, what is the next step in evaluating g(f(7))?

• Find f(3)

• Find f(-3)

• Find g(-3)

• Find g(3)

What is the final value of g(f(7))?

• 0

• 7

• 3

• -3

In the expression g(f(-6)), what is the first step?

• Find the value of f at x = 6

• Find the value of f at x = -6

• Find the value of g at x = -6

• Find the value of g at x = 6