Composition of Functions and Modeling

Question 1

A retailer is having a promotional sale for 35% off all items. There is a 7% sales tax added to the price. Which represents the situation, where x is the original cost of the item(s)?

Revolt · Accepted Answer

f(x) = 1.07x represents the price after taxes and g(x) = 0.65x represents the discount price. The total price would be (f ∘ g)(x) = 1.07(0.65x) = 0.6955x.

Question 2

If the area of the square is A(s) = s², find the formula for the area as a function of time, and then determine A(s(3)). A(t) equals t² + t + 625. The area of the square image after 3 seconds is square pixels.

Revolt · Accepted Answer

Part 1: 100; Part 2: 500; Part 3: 3,025

Question 3

Question 168702

Revolt · Accepted Answer

500

Question 4

Question 168703

Revolt · Accepted Answer

3,025

Question 5

Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true?

Revolt · Accepted Answer

-1; 10

Question 6

Question 168710

Revolt · Accepted Answer

10

Composition of Functions and Modeling Answers

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