Evaluating Composite Functions Concepts

This lesson introduces the concept of composition of functions, a new topic for students. It begins with evaluating single functions, using G of 2 as an example. The lesson then explains composite functions, where one function is inside another, and demonstrates two methods for evaluating them: evaluating each function step-by-step or finding the composite function first. The lesson includes examples of both methods, emphasizing the importance of understanding both approaches. Finally, it provides practice with different function combinations, such as F of J, to reinforce the concepts.

What is the main focus of lesson three in the unit?

• Graphing functions

• Composition of functions

• Solving equations

• Inverse of functions

How do you evaluate a function like G of 2?

• By dividing the function by 2

• By substituting 2 for X in the function

• By multiplying the function by 2

• By adding 2 to the function

What is the first step in evaluating a composite function?

• Evaluate the outer function first

• Evaluate the inner function first

• Add the two functions together

• Subtract the inner function from the outer function

What is the result of evaluating H of G of 2 using the step-by-step method?

• 0

• -1

• 1

• 2

Which method involves finding the composite function first before evaluating?

• Step-by-step evaluation

• Inverse function evaluation

• Direct substitution

• Composite function evaluation

What is the result of simplifying the composite function H of G of X?

• x - 2

• 2x - 5

• 2x - 7

• 2x - 3

What is the purpose of leaving a blank in the outer function during composition?

• To add a constant

• To insert the inner function

• To simplify the function

• To evaluate the function

In the example with F and J, what is the outer function?

• Function F

• Function H

• Function G

• Function J

What is the simplified form of the composite function F of J of X?

• 25x^2 + 8

• 25x^4 + 8

• x^2 + 8

• 5x^2 + 8

Which function is used as the inner function in the example with F and J?

• Function H

• Function F

• Function G

• Function J