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

Vertical Asymptotes of Rational Functions — Unit test Answers

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What is the solution to the equation ?

y = –4 and y = 4

y = 0

all real numbers

no solution

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Which graph represents the function ?

On a coordinate plane, a hyperbola and parabola are shown. The hyperbola has a curve in quadrants 1 and 2. The parabola opens down and has a vertex at (0, 0).

On a coordinate plane, a hyperbola and a cubic functions are shown. They hyperbola has curves in quadrants 1 and 3, and the cubic function goes through (0, 0).

On a coordinate plane, a hyperbola is shown. One curve is in quadrant 1 and the other curves goes through quadrants 2 and 4.

On a coordinate plane, a hyperbola is shown. Both curves open downward in quadrants 3 and 4.

Max can mow a lawn in 45 minutes. Jan takes twice as long to mow the same lawn. If they work together, the situation can be modeled by the following equation, where t is the number of minutes it would take to mow the lawn together.How long will it take Maxine and Jan to mow the lawn together?

30.0 minutes

45.0 minutes

67.5 minutes

135.0 minutes

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

There are asymptotes at and .

There are holes at and .

There are asymptotes at and .

There are holes at and .

How does the graph of compare to the graph of the parent function ?

g(x) is shifted 4 units right and 6 units up from f(x).

g(x) is shifted 4 units right and 6 units down from f(x).

g(x) is shifted 4 units left and 6 units up from f(x).

g(x) is shifted 4 units left and 6 units down from f(x).

Which function is undefined for x = 0?

y = RootIndex 3 StartRoot x minus 2 EndRoot

y = StartRoot x minus 2 EndRoot

y = RootIndex 3 StartRoot x + 2 EndRoot

y = StartRoot x + 2 EndRoot

Which of the following describes the graph of compared to the parent cube root function?

stretched by a factor of 2 and translated 64 units right and 5 units down

stretched by a factor of 8 and translated 8 units right and 5 units down

stretched by a factor of 2 and translated 8 units right and 5 units down

stretched by a factor of 8 and translated 64 units right and 5 units down

Where are the vertical asymptotes for the following function located?

x = –4 and x = 6

x = –4 and x = 7

x = 4 and x = –6

x = 6 and x = 7

Ted can clear a football field of debris in 3 hours. Jacob can clear the same field in 2 hours. When they work together, the situation can be modeled by the equation, where t is the number of hours it would take to clear the field together.How long will it take Ted and Jacob to clear the field together?

12 minutes

50 minutes

1 hour 12 minutes

2 hours 30 minutes

If the range of and the range of are the same, which statement is true about the value of m?

m can only equal 1.

m can be any positive real number.

m can be any negative real number.

m can be any real number.

The inverse variation equation shows the relationship for a cruise ship’s travel between the rate of travel, x, and the time to travel, y for a distance of 600 miles. What is the rate of travel in miles per hour (mph) if the trip takes 24 hours?

2.5 mph

25 mph

144 mph

14,400 mph

The equation shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?

The density approaches infinity.

The density approaches 0.

The density approaches 1.

The density approaches 13.

How many extraneous solutions does the equation below have?

Which of the following is the graph of ?

On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4. It starts at x = 3.

On a coordinate plane, an absolute value curve opens down and to the left in quadrants 1 and 2. It starts at x = 3.

On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2. It starts at x = negative 3.

On a coordinate plane, an absolute value curve opens up and to the right in quadrants 3 and 4. It starts at x = negative 3.

The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function , where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?

The horizontal asymptote of y = 0 means that the person’s temperature will approach 98.6ºF as time elapses.

The horizontal asymptote of y = 0 means that the person’s temperature will approach 0ºF as time elapses.

The horizontal asymptote of y = 4 means that the person’s temperature will approach 102.6ºF as time elapses.

The horizontal asymptote of y = 4 means that the person’s temperature will approach 4ºF as time elapses.

Which graph represents the function ?

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the right in quadrant 1, and another curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0.25.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.

On a coordinate plane, a hyperbola is shown. A curve opens up and to the left in quadrant 2, and another curve opens down and to the right in quadrant 4. A vertical asymptote is at x = 0.25.

Which statement describes the behavior of the function ?

The graph approaches –2 as x approaches infinity.

The graph approaches 0 as x approaches infinity.

The graph approaches 1 as x approaches infinity.

The graph approaches 2 as x approaches infinity.

What are the removable discontinuities of the following function?

x = –6, x = 0, and x = 6

x = –6 and x = 6

x = 0 and x = –6

x = 0 and x = 6

Kent multiplies both sides of the equation below by an expression.Then he moves all the terms to one side of the equal sign in the resulting equation. Which equation must he solve now?