Function Composition and Evaluation

This video tutorial explains how to evaluate the composition of three functions, f, g, and h, using two methods: direct substitution and a more efficient step-by-step approach. It also demonstrates how to use a data table to evaluate function compositions. The tutorial provides clear examples and calculations to help learners understand the process.

What is the main focus of this lesson?

• Studying linear functions

• Learning about derivatives

• Understanding the composition of three functions

• Solving quadratic equations

Which function is substituted first in the composition F(G(H(x)))?

• F(x)

• None of the above

• H(x)

• G(x)

What is the result of evaluating H(2) in the example?

• 18

• 16

• 12

• 10

Which method is described as easier for evaluating F(G(H(2)))?

• First method

• Second method

• Neither method is easy

• Both methods are equally easy

What is the value of G(16) in the example?

• 8

• 6

• 4

• 2

What is the purpose of using a data table in this lesson?

• To solve linear equations

• To evaluate compositions of functions

• To calculate integrals

• To find derivatives

In the data table example, what is the value of F(2)?

• 7

• 3

• 9

• 5

What is the final result of evaluating H(F(G(2))) using the data table?

• 1

• 0

• 2

• 3

Which function is evaluated last in the composition H(F(G(2)))?

• None of the above

• G(x)

• F(x)

• H(x)

What is the intersection value of G and 4 in the data table?

• 2

• 3

• 1

• 4