Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Graphing Rational Functions

Unit Test Answers

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Using V = lwh, what is an expression for the volume of the following rectangular prism?

StartFraction 15 Over 2 x EndFraction

StartFraction 3 x + 12 Over 2 x + 8 EndFraction

StartFraction 15 Over 2 x + 2 EndFraction

Fifteen-eighths

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Mr. Knotts found the difference of the following expression. Which statement is true about Mr. Knotts’s work? Step 1: Step 2: Step 3: Step 4:

In step 1, he did not correctly factor the denominator.

In step 2, he did not use the correct common denominator.

In step 3, he did not distribute the negative sign when he subtracted.

In step 4, he did not correctly subtract the numerator.

A basketball player’s free-throw percentage is the ratio of the number of successful shots made to the number of shots attempted. A basketball player has made 13 of the first 20 free throws she has attempted this season. Which rational expression can be used to find the free throw percentage for the season if she successfully makes her next x free-throw attempts?

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What is the solution to the equation ?

y = –4 and y = 4

y = 0

all real numbers

no solution

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?

The resistance approaches 0.

The resistance approaches .

The resistance approaches L.

The resistance approaches infinity.

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

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

There is a hole at x = 2.

There are asymptotes at x = 0 and x = –1.

There are asymptotes at x = 0 and x = –1 and a hole at .

There are holes at x = 0 and x = –1 and an asymptote at x = 2.

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What is the solution to the equation ?

m = –4

m = –2

m = 2

m = 4

Which of the following is always irrational?

the sum of two fractions

the product of a fraction and a repeating decimal

the sum of a terminating decimal and the square root of a perfect square

the product of a repeating decimal and the square root of a non-perfect square

Which of the following expresses as a fraction in simplest form?

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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.

Which number is rational?

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9.23157 ...

The table below shows y, the average speed of a cyclist in miles per hour, and x, the time in hours that it takes the cyclist to complete a bicycle tour. Which rational function best models the data in the table?Time, x(hours)Average Speed, y(miles per hour)128166918

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What is the product?

StartFraction k + 1 Over k squared EndFraction

StartFraction k minus 1 Over k squared EndFraction

StartFraction negative 1 Over k EndFraction

StartFraction 1 Over k EndFraction

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).

The product of a non-zero rational number and an irrational number can always be written as

a fraction.

a terminating decimal.

a non-repeating, non-terminating decimal.

a repeating decimal

Which expression is equivalent to the expression below?

StartFraction 1 Over (m + 4) (m + 3) EndFraction

StartFraction 1 Over (m minus 4) (m minus 3) EndFraction

StartFraction m minus 4 Over m minus 3 EndFraction

StartFraction m + 3 Over m + 4 EndFraction

Which expression is equivalent to the expression below?

StartFraction 3 c (2 c minus 1) Over 2 c + 1 EndFraction

StartFraction negative 3 c (2 c + 1) squared Over 4 (2 c minus 1) squared EndFraction

–3c

Which expression is equivalent to the following complex fraction?

StartFraction negative 2 y + 5 x Over 3 x minus 2 y EndFraction

StartFraction 3 x minus 2 y Over negative 2 y + 5 x EndFraction

StartFraction x squared y squared Over (negative 2 y + 5 x) (3 x minus 2 y) EndFraction

StartFraction (negative 2 y + 5 x) (3 x minus 2 y) Over x squared y squared EndFraction

Which expression is equivalent to the following complex fraction?

StartFraction y + x Over y minus x EndFraction

StartFraction (y minus x) (y + x) Over x squared y squared EndFraction

StartFraction x squared y squared Over (y + x) (y + x) EndFraction

StartFraction y minus x Over y + x EndFraction

Which expression is equivalent to ?

StartFraction m minus 4 Over (m + 4) (m + 2) EndFraction

StartFraction (m + 4) (m + 2) Over m minus 4 EndFraction

StartFraction (m minus 4) (m + 2) Over m + 4 EndFraction

StartFraction m + 4 Over (m minus 4) (m + 2) EndFraction

What is the quotient?

StartFraction 1 Over 2 y EnDfraction

StartFraction 3 y + 2 Over 6 y squared EndFraction

StartFraction 1 Over y EndFraction

StartFraction 2 (3 y + 2) Over 3 EndFraction

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.

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?

The high school option costs less per class for six classes.

The gym option costs less per class for six classes.

The high school option costs less per class for seven classes.

The gym option costs less per class for seven classes.

Marshall bought 32 ounces of mixed nuts, which are estimated to be 30% peanuts. Which expression can be used to find the percentage of peanut concentration of the final mix if he adds x ounces of peanuts?

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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?

a = –1, m = 0

a = 1, m = 0

a = –1, m = 1

a = 1, m = 1

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

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?

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.

The horizontal asymptote of y = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

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.

The vertical asymptote of x = 0 represents that the average cost per unit will approach $0 as the number of units produced increases.

What is the product?

StartFraction 4 n Over n + 1 EndFraction

StartFraction n Over n + 1 EndFraction

StartFraction 1 Over n + 1 EndFraction

StartFraction 4 Over n + 1 EndFraction

Using V = lwh, what is an expression for the volume of the following prism?

StartFraction 4 (d minus 2) Over 3 (d minus 3)(d minus 4) EndFraction

StartFraction 4 d minus 8 Over 3 (d minus 4) squared EndFraction

StartFraction 4 Over 3 d minus 12 EndFraction

StartFraction 1 Over 3 d minus 3 EndFraction

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.

Megan borrowed $50,000 at 5% simple interest for 6 years. Joseph borrowed $60,000 at 4% simple interest for 8 years. The formula can be used to calculate the monthly payment, m, where P is the principle amount borrowed, r is the rate expressed as a decimal, and t is the amount of time for the loan, in years. Who will have a greater monthly payment, and by how much?

Megan will pay approximately $8 dollars more per month.

Megan will pay approximately $78 dollars more per month

Joseph will pay approximately $8 dollars more per month.

Joseph will pay approximately $78 dollars more per month.

Sam is determining the area of a triangle. In this triangle, the value for the height is a terminating decimal, and the value for the base is a repeating decimal. What can be concluded about the area of this triangle?

The area will be irrational because the height is irrational.

The area is irrational because the numbers in the formula are irrational and the numbers substituted into the formula are rational.

The area is rational because the numbers in the formula are rational and the numbers substituted into the formula are rational.

The area will be rational because both the height and the base are irrational.

How many extraneous solutions does the equation below have?

Which number expresses 6.72 as a fraction in simplest form?

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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

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

The cost of catering a dinner is $11.95 per person plus $25 for delivery and setup. Which statement is true about the graph of the function that represents the average cost per person?

The horizontal asymptote y = 0 represents that the cost per person approaches $0 as the number of people increases.

The horizontal asymptote y = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

The vertical asymptote x = 0 represents that the cost per person approaches $0 as the number of people increases.

The vertical asymptote x = 11.95 represents that the cost per person approaches $11.95 as the number of people increases.

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.

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