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Performance Task: Production Schemes — Unit test Answers

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For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?

Question illustration
A
a = –1, m = 0
B
a = 1, m = 0
C
a = –1, m = 1
D
a = 1, m = 1
2
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A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?

A
exactly 5
B
5 or less
C
exactly 6
D
6 or less
3

Identify the horizontal and vertical asymptotes, if any, for the graph of f(x) shown. Check all that apply.

A
y = 0
B
y = 1
C
x = 1
D
x = –1
E
no vertical asymptotes
F
no horizontal asymptotes
4

Which statement is true about ?

Question illustration
A
The graph of f(x) has a vertex of (–3, 2).
B
The graph of f(x) is a horizontal compression of the graph of the parent function.
C
The graph of f(x) opens downward.
D
The graph of f(x) has range of f(x) –2.
Option D
5

Given the function f(x) = –5|x + 1| + 3, for what values of x is f(x) = –12?

A
x = –2, x = –4
B
x = –2, x = 4
C
x = 2, x = –4
D
x = 2, x = 4
6

A polynomial function has a root of –6 with multiplicity 3 and a root of 2 with multiplicity 4. If the function has a negative leading coefficient and is of odd degree, which could be the graph of the function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

What are the vertical and horizontal asymptotes for the function ?

Question illustration
A
vertical asymptote: x = 1horizontal asymptote: none
B
vertical asymptote: x = 1horizontal asymptote: y = 0
C
vertical asymptote: x = –2, x = 3horizontal asymptote: y = 0
D
vertical asymptote: x = –2, x = –3horizontal asymptote: none
9

Which is the graph of reflected across the x-axis, translated 3 units left, 4 units up, and dilated by a factor of 4?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

A polynomial function has a root of –7 with multiplicity 2, a root of –1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?

A
The graph of the function is positive on (2, 4).
B
The graph of the function is negative on (4, ).
Option B
C
The graph of the function is positive on (, –7).
Option C
D
The graph of the function is negative on (–7, –1).
11

Which statements comparing the graphs of function 1 and function 2 are true? Check all that apply.

A
Function 1 has a hole, while function 2 does not.
B
Function 1 has an oblique asymptote, while function 2 does not.
C
Function 2 has a hole, while function 1 only has asymptotes.
D
Function 2 only has asymptotes, while function 1 has a hole.
E
Both functions have the same domain restriction.
F
Both functions have the same vertical asymptote.
12

The president of a company creates a graph of the price of the company’s stock over one year. He describes the graph as follows:• The price of the stock rose to about $17 before falling to about $3.• There have only been two periods during which the price of the stock decreased.• The price of the stock is expected to increase in the long run.Which graph correctly shows the price of the stock?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
13

Which statement comparing the oblique asymptotes of the functions f(x) and g(x) is true?

Question illustration
A
The oblique asymptote for g(x) is steeper than for f(x).
B
Both functions have the same oblique asymptote.
C
The oblique asymptote for f(x) is steeper than for g(x).
D
Both functions have parallel oblique asymptotes.
14

For the inverse variation equation xy = k, what is the constant of variation, k, when x = –2 and y = 5?

A
–10
B
Negative two-fifths
Option B
C
Five-halves
Option C
D
10
15

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

Question illustration
A
f(x) = x(x – a)2(x – b)4
B
f(x) = x(x – a)3(x – b)2
C
f(x) = x4(x – a)(x – b)2
D
f(x) = x2(x – a)5(x – b)

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