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

A square image of an object on a video game has an initial side length of 25 pixels. To make the object appear closer, the side length of the square is increased by 10 pixels per second. This length change is represented by the function s(t) = 25 + 10t, where t is time in seconds.

Revolt · Accepted Answer

A(t): 100; +: 500; 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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