AnswersAISD Algebra II B Credit Recovery 2026-2027Vertical Asymptotes of Rational Functions

Vertical Asymptotes of Rational Functions — Unit test Answers

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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
2
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Which statement is true about the discontinuities of the function f(x)?

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

Which function has a domain of and a range of ?

Question illustration
A
y = StartRoot x minus 5 EndRoot + 3
Option A
B
y = StartRoot x + 5 EndRoot minus 3
Option B
C
y = negative StartRoot x minus 5 EndRoot + 3
Option C
D
y = negative StartRoot x + 5 EndRoot minus 3
Option D
4

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
5

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.
6

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

Question illustration
A
StartFraction 1 Over 32 EndFraction
Option A
B
One-half
Option B
C
2
D
32
7

Haji rows his canoe 10 mph in still water. He noticed one day that he could row 4 miles upstream in the same amount of time he could row 6 miles downstream. What was the approximate speed of the current that day?

A
2.0 mph
B
3.3 mph
C
5.0 mph
D
10.0 mph
8

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
9

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.
10

What is the solution to the equation ?

Question illustration
A
m = –4
B
m = –2
C
m = 2
D
m = 4
11

Which of the following is the graph of ?

Question illustration
A
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = negative 1.
Option A
B
On a coordinate plane, an absolute value curve curves up and to the right in quadrant 4 and starts at y = 1.
Option B
C
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = 1.
Option C
D
On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2 and starts at y = negative 1.
Option D
12

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
13

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
14

Which graph represents ?

Question illustration
A
On a coordinate plane, a cubic function has an inflection point at (0, negative 2).
Option A
B
On a coordinate plane, a cubic function has an inflection point at (negative 2, 0)
Option B
C
On a coordinate plane, a cubic function has an inflection point at (0, 2).
Option C
D
On a coordinate plane, a cubic function has an inflection point at (2, 0).
Option D
15

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

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