Evaluating Composite Functions

The video tutorial explains how to evaluate composite functions using a table of values, a graph, and a function rule. It provides three examples: calculating G(f(-2)), F(G(2-1)), and H(F(1)-3). Each example demonstrates the process of determining inner function values and using them to find the composite function value. The tutorial emphasizes understanding the relationship between input and output values in different representations.

What are the three representations used to evaluate composite functions in this tutorial?

• Table, graph, and function rule

• Equation, graph, and table

• Table, list, and equation

• Graph, equation, and list

In the first example, what is the value of f(-2) according to the table?

• -1

• 0

• 1

• 2

What is the value of G(1) in the first example?

• 2

• 0

• 3

• 1

In the second example, what is the inner function value G(1)?

• 0

• 1

• 2

• 3

What is the final composite function value for F(G(2-1))?

• 3

• 0

• 1

• 2

In the third example, what is the value of f(1) according to the table?

• 0

• 1

• 2

• 3

What is the expression used to find H(0) in the third example?

• x^2 + 2

• x^2 - 2

• x^2 - 3

• x^2 + 3

What is the final composite function value for H(f(1)-3)?

• 0

• 6

• 3

• -3

Which of the following is NOT a step in evaluating composite functions?

• Use a graph to find the output

• Use a table to find the output

• Determine the inner function value

• Multiply the function values

What is the purpose of using different representations like tables and graphs in evaluating composite functions?

• To make the process more complex

• To verify the results through different methods

• To confuse the students

• To avoid using equations