AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Vertical Asymptotes of Rational Functions

Vertical Asymptotes of Rational Functions — Unit test Answers

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Naomi wants to take yoga classes. She can take classes at the high school for a one-time fee of $20 plus $10 per class. She can join the local gym for $50 and take classes for $5 per class. Which statement is true about the average cost for the two options?

A
The high school option costs less per class for six classes.
B
The gym option costs less per class for six classes.
C
The high school option costs less per class for seven classes.
D
The gym option costs less per class for seven classes.
2
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Which statement is true about the discontinuities of the function f(x)?

Question illustration
T
There is a hole at x = 2.
T
There are asymptotes at x = 0 and x = –1.
T
There are asymptotes at x = 0 and x = –1 and a hole at .
Option T
T
There are holes at x = 0 and x = –1 and an asymptote at x = 2.
3

A certain company has a fixed cost of $200 per day. It costs the company $3.10 per unit to make its products. The company is tracking its average cost to make x units using . Which statement is true?

Question illustration
A
The horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
B
The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
C
The vertical asymptote of x = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.
D
The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.
4

For the inverse variation equation , what is the value of p when V = ?

Question illustration
A
Option
Option A
B
Option
Option B
2
2
3
32
5

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
a
a = 1, m = 0
a
a = –1, m = 1
a
a = 1, m = 1
6

Lupe can ride her bike at a rate of 20 mph when there is no wind. On one particular day, she rode 2 miles against the wind and noticed that it took her the same amount of time as it did to ride 3 miles with the wind. How fast was the wind blowing that day?

A
4 mph
B
7 mph
C
10 mph
D
12 mph
7

Which graph represents the function ?

Question illustration
A
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = negative 2.
Option A
B
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = negative 2.
Option B
C
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens down and to the left in quadrants 2 and 3. A vertical asymptote is at x = negative 3, and the horizontal asymptote is at y = 2.
Option C
D
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1 , and the other curve opens down and to the left in quadrants 2, 1, and 4. A vertical asymptote is at x = 3, and the horizontal asymptote is at y = 2.
Option D
8

Which expression is equivalent to the expression below?

Question illustration
A
StartFraction 3 c (2 c minus 1) Over 2 c + 1 EndFraction
Option A
B
StartFraction negative 3 c (2 c + 1) squared Over 4 (2 c minus 1) squared EndFraction
Option B
C
3c
D
–3c
9

What is the product?

Question illustration
A
StartFraction k + 1 Over k squared EndFraction
Option A
B
StartFraction k minus 1 Over k squared EndFraction
Option B
C
StartFraction negative 1 Over k EndFraction
Option C
D
StartFraction 1 Over k EndFraction
Option D
10

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.
11

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
12

The resistance, R, to electricity of a cylindrical-shaped wire is given by the equation , where p represents the resistivity of the wire’s material, L represents the length of the wire, and d represents the diameter of the wire. What happens to the resistance of the wire as the diameter approaches 0?

Question illustration
A
The resistance approaches 0.
B
The resistance approaches .
Option B
C
The resistance approaches L.
D
The resistance approaches infinity.
13

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
14

What is the quotient?

Question illustration
A
StartFraction 1 Over 2 y EnDfraction
Option A
B
StartFraction 3 y + 2 Over 6 y squared EndFraction
Option B
C
StartFraction 1 Over y EndFraction
Option C
D
StartFraction 2 (3 y + 2) Over 3 EndFraction
Option D
15

Which solution to the equation is extraneous?

Question illustration
A
a = –2
B
a = –2 and a = 4
C
neither a = –2 nor a = 4
D
a = 4

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