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

Question 7

Which statements are true regarding the functions described? Check all that apply.

Revolt · Accepted Answer

The domain of V(h(r)) is restricted to values of r greater than 0.; V(h(r)) = 3.5πr3; The volume depends on the radius of the cylinder.

Question 8

What is the selling price per widget as a function of the number of widgets produced, and what should the selling price be if 15 widgets are produced?

Revolt · Accepted Answer

S(C(x)) = –0.14x2 + 140; $108.50

Question 9

Which statement describes function composition with respect to the commutative property?

Revolt · Accepted Answer

Given f(x) = 4x and g(x) = x², (f ∘ g)(x) = 4x² and (g ∘ f)(x) = 16x², so function composition is not commutative.

Question 10

The compositions f(g(x)) and g(f(x)) of functions f and g are shown on the graph. Which statements describe the compositions? Check all that apply.

Revolt · Accepted Answer

f(g(x)) = g(f(x)) for at least one value of x.; f(g(0)) = 5 and g(f(–2.5)) = 5.; Both f(g(x)) and g(f(x)) have the same domain.; The graphs show that function composition is not commutative.

Composition of Functions and Modeling Answers

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