2025 Benchmark 3 Review

Benchmark Review Practice Test

Open Ended

A school is evaluating two transportation options for a field trip. 

• Plan A: The first company's scheduling inefficiencies cause the total cost to increase rapidly as more students are added. This cost is modeled by Cost A = $$2x^2$$ .

• Plan B: The second company charges $2 per student plus a $40 flat fee.

Let x be the number of students attending. 

 

For what values of x is Plan A less expensive than Plan B?

 

 

Enter your answer and your work and explanation in the space provided. You may also use the drawing tool to help explain or support your answer.

Multiple Choice

What extraneous solution arises when solving for the point of intersection of the line $$f\left(x\right)=\frac{1}{2}x+2$$ and the square root function $$f\left(x\right)=\sqrt[\ ]{x+7}$$

• x = 2

• x = 6

• x = -2

• x = -6

Multiple Choice

Which of the following statements is true about the solutions of $$\frac{x}{x-2}-\frac{4}{x+3}=\frac{10}{x^2+x-6}$$

• There are two solutions x = 2 and x = -1

• There is one solution: x = 2

  x = -1 is extraneous

• There is one solution: x = -1

  x = 2 is extraneous

• There are no solutions.

Multiple Choice

Identify the zeros and asymptotes of $$f\left(x\right)=\frac{2x^2-8}{x^2-9}$$

• Zeros: -3 and 3

  Vertical Asymptotes:

  x = -2 and x = 2

  Horizontal Asymptotes:

  y = 2

• Zeros: -2 and 2

  Vertical Asymptotes:

  x = -3 and x = 3

  Horizontal Asymptotes:

  y = 1

• Zeros: -2 and 2

  Vertical Asymptotes:

  x = -3 and x = 3

  Horizontal Asymptotes:

  y = 2

• Zeros: -3 and 3

  Vertical Asymptotes:

  x = -2 and x = 2

  Horizontal Asymptotes:

  y = 1

Multiple Choice

A student is given the following square root equation:

$$\sqrt[\ ]{2-x}=x+4$$

The student correctly solves the equation and finds the solutions $$x=-2$$ or $$x=-7$$ .

Which best describes the solution set to the original equation?

• x = -7 is the only solution because x = -2 is extraneous.

• x = -2 is the only solution because x = -7 is extraneous.

• The equation has two solutions, both x = -2 and x = -7.

• The equation has no solutions since both x = -2 and x = -7 are extraneous.

Multiple Choice

Which number line graph shows the solutions to the following inequality?

$$x^2+6<7x$$

• T

• The number line graph should show a closed interval between 1 and 6.

Multiple Choice

Solve for x

$$\frac{1}{x-2}=\frac{x}{x^2-4}$$

• x is all real numbers

• There are no solutions to the equation.

• x = 2

• x = -2

Multiple Select

The time in hours, y, required to travel 100 miles is inversely proportional to the rate at which the car travels in miles per hour, x. Which of the following statements correctly interpret features of the graph representing this situation? Select all that apply.

• As the rate decreases, the time required also decreases.

• As the rate increases, the time required also decreases.

• The point (2, 50) means it would take 2 hours to travel 50 miles.

• 
  The point (80, 1.25) means it would take 1.25 hours to travel 100 miles at 80 mph.

• There is a horizontal asymptote at $$y=0$$

This is correct because as you are looking at the graph rate is your x, so the x is getting bigger, then the time which is your y is decreasing

​As the rate increases, the time required also decreases.

The point (80, 1.25) means it would take 1.25 hours to travel 100 miles at 80 mph.

This is correct because x is the rate (miles per hour) and y is the time (hours).

Multiple Choice

A painter estimates she can paint a house in 40 hours. She thinks her assistant can do the job in 60 hours. How long would it take them to paint the house working together?

• 20 hours

• 24 hours

• 50 hours

• 100 hours

Drag and Drop

Let $$f(x)=5\sqrt[]{x-7}-4$$ . To graph f(x), you could use the graph of g(x)=√x and then perform a horizontal translation of h units, a vertical stretch of a units, and a vertical translation of h units. What are the values of h, a, and k?



h=​ ​

Placeholder

a=​

Placeholder

k= ​

Placeholder

Drag these tiles and drop them in the correct blank above

7

-7

5

1/5

-4

4

Multiple Choice

Which of the following functions has a horizontal asymptote at y=-6 and a vertical asymptote at x=4

• $$f\left(x\right)=\frac{3}{x+6}-4$$

• $$f\left(x\right)=\frac{3}{x-6}-4$$

• $$f\left(x\right)=\frac{3}{x-6}-4$$

• $$f\left(x\right)=\frac{3}{x-4}-6$$

• $$f\left(x\right)=\frac{3}{x+4}+6$$

Multiple Choice

What is the solution to the inequality $$2x^2+7x+3<3$$

• x<-3

  or

  x>0

• x>-3

  or

  x<0

• -3<x<0

• 0<x<-3