AnswersAlgebra 2 SAT 26-27 Supplemental Wk3Inverse of a Function

Inverse of a Function — Unit test Answers

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Suppose . Which value(s) of a would make the composite functions commutative?

Question illustration
A
0
B
2
C
any value of a
D
no value of a
2
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Study the graphs of f(x) and g(x).

Question illustration
A
Vertical stretch followed by a translation 1 unit left, so g(x) = f.
Option A
B
Vertical stretch followed by a translation 1 unit right, so g(x) = f.
Option B
C
Horizontal stretch followed by a translation 1 unit left, so g(x) = f.
Option C
D
Horizontal stretch followed by a translation 1 unit right, so g(x) = f.
Option D
3

Consider the function f(x) = 10(x2 – 7x). What are the additive and multiplicative inverses?

A
The additive inverse is g(x) = 10(x2 + 7x) and the multiplicative inverse is h(x) =.
Option A
B
The additive inverse is g(x) = –10(x2 – 7x) and the multiplicative inverse is h(x) =.
Option B
C
The additive inverse is g(x) = 10(x2 + 7x) and the multiplicative inverse is h(x) = .
Option C
D
The additive inverse is g(x) = –10(x2 – 7x) and the multiplicative inverse is h(x) = .
Option D
4

Suppose f(x) = 2(x + 1)2 and f(g(x)) = 2(2x + 4)2. What is g(x)?

A
g(x) = x + 3
B
g(x) = x + 4
C
g(x) = 2x + 3
D
g(x) = 2x + 4
5

For the function q(x) =, what is the inverse function?

Question illustration
A
q–1(x) =
Option A
B
q–1(x) =
Option B
C
q–1(x) =
Option C
D
q–1(x) =
Option D
6

Which is the graph of y =-3 ?

Question illustration
A
On a coordinate plane, a curve starts at (0, 0) and curves up through (negative 3, 3).
Option A
B
On a coordinate plane, a curve starts at (0, 0) and curves down through (1, negative 1) and (4, negative 2).
Option B
C
On a coordinate plane, a curve starts at (0, 0) and curves down through (1, negative 3).
Option C
D
On a coordinate plane, a curve starts at (0, 0) and curves up through (1, 3) and (2, 4.5).
Option D
7

On March 24, 1989, the Exxon Valdez oil tanker ran aground and leaked millions of gallons of oil into Prince William Sound. The spill covered approximately 11,000 square miles of ocean. The oil spread out in a circular pattern and the radius increased by 0.10 mph. Use π = 3.14.At this rate, how many hours did it take for oil to cover the area?

A
187 hours
B
592 hours
C
1,871 hours
D
5,917 hours
8

Consider the function represented in the table.

Question illustration
A
(–20, 8)
B
(–10, 3)
C
(0, –2)
D
(8, –6)
9

The function h(x) = –x5 + 12x is an odd function. Which transformation of h(x) results in an odd function?

A
h(5 – x)
B
1 + h(x)
C
h(x + 8)
D
–6h(x)
10

Which single transformation can be applied to the graph of y = 72 to produce the graph of y = 9 ?

Question illustration
A
vertical translation
B
vertical compression
C
horizontal translation
D
horizontal compression
11

Marie spends $450.00 at a department store. She has two coupons: one for a 15% discount and one for $50 off any purchase above $300. The store allows the coupons to be combined. Which coupon should be applied first, and what is the final purchase price?

A
Apply the 15% discount first, and the final purchase price is $332.50.
B
Apply the 15% discount first, and the final purchase price is $340.00.
C
Apply the $50 off first, and the final purchase price is $332.50.
D
Apply the $50 off first, and the final purchase price is $340.00.
12

Consider the inverse function. Which conclusions can be drawn about f(x) = x2 + 2? Select three options.f(x) has a limited range.f(x) has a restricted domain.f(x) has an x-intercept of (2, 0).f(x) has a maximum at the point (0, 2).f(x) has a y-intercept at the point (0, 2).

Question illustration
A
f(x) has a limited range.
B
f(x) has a restricted domain.
C
f(x) has an x-intercept of (2, 0).
D
f(x) has a maximum at the point (0, 2).
E
f(x) has a y-intercept at the point (0, 2).
13

How can the graphs of f(x) = and g(x) = be used to prove that f(x) and g(x) are inverse functions?

Question illustration
A
Show that the graph of g(x) is a translation of the graph of f(x).
B
Show that the graph of g(x) is a rotation about the origin of the graph of f(x).
C
Show that the graph of g(x) is a reflection about the x-axis of the graph of f(x).
D
Show that the graph of g(x) is a reflection about the line y = x of the graph of f(x).
14

Consider the function.f(x) = x2 + 3Which answer pairs a possible domain restriction that if placed upon f(x) would impact f–1(x) as shown?

A
f(x) domain: x ≥ 3f–1(x) domain: x ≥ 3
B
f(x) domain: x ≥ 3f–1(x) range: y ≥ 3
C
f(x) domain: x ≥ 0f–1(x) domain: x ≥ 0
D
f(x) domain: x ≥ 0f–1(x) range: y ≥ 0
15

In a physics class, the teacher proposes that the velocity of a car in miles per hour and the stopping distance in feet are represented by inverse functions.Assuming this is true, which graph includes a pair of functions for a specific velocity function and the corresponding stopping distance that can be verified as inverses?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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