AnswersFL-1200330-Algebra 2 CRModeling with Rational Functions

Modeling with Rational Functions — Unit test Answers

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Find the vertical, horizontal, and slant asymptotes, if any, for

Question illustration
A
vertical: horizontal: y = 0
B
horizontal: y = 0slant:
C
vertical: slant:
D
vertical: slant:
2
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Determine the asymptotes of the function:

Question illustration
A
horizontal: , slant:
B
horizontal: , slant:
C
vertical: , slant:
D
vertical: x = 1, x = 3 slant:
3

The slant asymptote of is .

Question illustration
A
T
B
F
4

Determine the equations of the vertical and horizontal asymptotes, if any, for .a., c., b.d.

Question illustration
A
A
B
B
C
C
D
D
5

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
6

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
7

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
8

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
9

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
10

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.
11

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.
12

Determine the equations of the vertical and horizontal asymptotes, if any, for .a., c., b.d.

Question illustration
A
A
B
B
C
C
D
D
13

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
14

Which expression is equivalent to the following complex fraction?

Question illustration
A
StartFraction x minus 3 Over x EndFraction
Option A
B
StartFraction x + 3 Over 1 EndFraction
Option B
C
StartFraction x + 3 Over x EndFraction
Option C
D
StartFraction x Over x + 3 EndFraction
Option D
15

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.
16

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
17

Determine the equations of the vertical and horizontal asymptotes, if any, for .a., c.b., d.,

Question illustration
A
A
B
B
C
C
D
D
18

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 .
C
The resistance approaches L.
D
The resistance approaches infinity.
19

The table below shows how the number of hours needed to fill a pool depends on the flow rate of the hoses used to fill it.Flow rate, x(gal/hr)Time, y(hours)60300454003650030600How long will it take to fill the pool if two hoses are used, one that fills at a rate of 40 gallons per hour and one that fills at a rate of 60 gallons per hour?

A
100 hours
B
150 hours
C
180 hours
D
200 hours
20

What is the solution to the equation ?

Question illustration
m
m = –4
m
m = –2
m
m = 2
m
m = 4

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