Question 1(Multiple Choice Worth 1 points)

Question

(02.03 HC)

The following table shows the amount of water leaking from an inflatable pool as a function of time:

Time (in minutes)
x Water (in liters)
f(x)
0 35
1 30
2 25
3 20
4 15

Find and interpret the meaning of the x-intercept in this scenario.
(7, 0); the time it takes to empty the water in the pool
(5, 0); the time it takes to empty the water in the pool
(5, 0); the time it takes to fill up the water in the pool
(7, 0); the time it takes to fill up the water in the pool
Question 2(Multiple Choice Worth 1 points)
(02.04 MC)

A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 10 of the recall, the manufacturer fixed 200 cars. In week 15, the manufacturer fixed 175 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic.

f(x) = 5x + 250
f(x) = −5x + 250
f(x) = 10x + 200
f(x) = −10x + 200
Question 3(Multiple Choice Worth 1 points)
(02.04 MC)

Choose the equation that represents the graph.

graph of a line passing through points negative 2 comma 0 and 0 comma negative 4

y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Question 4(Multiple Choice Worth 1 points)
(02.01 MC)

Given g(x) = − 4x + 8, identify the domain, range, and x-intercept of the function.

Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0)
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0)
Domain: −4 < x < 8; Range: − 4 < y < ∞; x-intercept (2, 0)
Domain: −4 < x < 8; Range: −∞ < y < 4; x-intercept (−2, 0)
Question 5(Multiple Choice Worth 1 points)
(02.05 MC)

The table represents the linear function f(x), and the equation represents the linear function g(x).

Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.

x f(x)
0 1
2 4
4 7

g(x) = 2x + 1
The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is greater than the y-intercept of g(x).
Question 6(Multiple Choice Worth 1 points)
(02.04 MC)

Write an equation of a line that is perpendicular to y = 3x + 3 and passes through (−6, 3).

y equals negative one-third times x plus 1
y equals negative one-third times x minus 5
y = 3x + 21
y = 3x − 15
Question 7(Multiple Choice Worth 1 points)
(02.05 LC)

Which of the following statements best describes the effect of replacing the graph of f(x) with the graph of f(x) − 5?

The graph shifts 5 units up.
The graph shifts 5 units down.
The graph shifts 5 units left.
The graph shifts 5 units right.
Question 8(Multiple Choice Worth 1 points)
(02.05 MC)

The equation represents Function A, and the graph represents Function B:

Function A

f(x) = x − 9

Function B

graph of line going through ordered pairs negative 1, negative 3 and 2, 3

Which equation best compares the slopes of the two functions?

Slope of Function B = 2 x Slope of Function A
Slope of Function A = Slope of Function B
Slope of Function A = 2 x Slope of Function B
Slope of Function B = − Slope of Function A
Question 9(Multiple Choice Worth 1 points)
(02.02 MC)

Given the function f(x) = −2x2 + 3x + 10, find f(1) and f(3). Choose the statement that is true concerning these two values.

The value of f(1) is the same as the value of f(3).
The value of f(1) cannot be compared to the value of f(3).
The value of f(1) is larger than the value of f(3).
The value of f(1) is smaller than the value of f(3).
Question 10(Multiple Choice Worth 1 points)
(02.02 MC)

A factory's production is modeled by function f(x), where f(x) is the number of parts produced per hour and x is the number of people working during production. Choose the ordered pair that represents a possible domain and range of the function.

(−1, 15)
(5, −50)
(−10, −100)
(5, 10)
Question 11(Multiple Choice Worth 1 points)
(02.03 MC)

The graph shows the velocity f(t) of a runner during a certain time interval:

Graph of line segment going through ordered pairs 0, 2 and 6, 8. Graph of another line segment going through ordered pairs 6, 8 and 8, 0. Label on the x axis is time in seconds, and label on the y axis is velocity in meters per second.

Which of the following describes the intercepts on the graph?

The initial velocity of the runner was 8 m/s, and the runner stopped after 2 seconds.
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.
The initial acceleration of the runner was 8 m/s2, and the runner stopped after 2 seconds.
The initial acceleration of the runner was 2 m/s2, and the runner stopped after 8 seconds.
Question 12(Multiple Choice Worth 1 points)
(02.02 LC)

If f(x) is the total cost, in dollars, of x candies, which of the following statements best describes the meaning of f(2) = 6?

The total cost of 2 candies is $6.
The total cost of 6 candies is $2.
The total cost of 2 candies is $3.
The total cost of 3 candies is $2.
Question 13(Multiple Choice Worth 1 points)
(02.03 MC)

A telephone company charges a fixed monthly rate plus a rate per megabyte of data used. The company charges $135 for 100 megabytes of data and $375 for 500 megabytes of data. An equation can be written to show the relationship between the total megabytes used (x) and the total monthly charges (y). Which of the following best describes the steps to draw the graph?

Draw a graph that joins the points (135, 100) and (375, 500) and has a slope = 0.6
Draw a graph that joins the points (100, 135) and (500, 375) and has a slope = 0.6
Draw a graph that joins the points (100, 135) and (500, 375) and has a slope = 1.67
Draw a graph that joins the points (135, 100) and (375, 500) and has a slope = 1.67
Question 14(Multiple Choice Worth 1 points)
(02.04 MC)

Choose the equation that represents the line passing through the point (−2, −3) with a slope of −6.

y = −6x − 15
y = −6x − 20
y = −6x + 15
y = −6x + 20
Question 15(Multiple Choice Worth 1 points)
(02.05 MC)

Determine the range of f(x) = |x| − 4.

{y | −∞ < y < ∞}
{y | −4 ≤ y < ∞}
{y | 0 < y < ∞}
{y | 4 < y < ∞}

Answer 1

Here are the answers to the multiple-choice questions:

Question 1:
(5, 0); the time it takes to empty the water in the pool

Question 2:
f(x) = −5x + 250

Question 3:
y = −2x + 4

Question 4:
Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0)

Question 5:
The slope of f(x) is less than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).

Question 6:
y equals negative one-third times x plus 1

Question 7:
The graph shifts 5 units down.

Question 8:
Slope of Function A = Slope of Function B

Question 9:
The value of f(1) is larger than the value of f(3).

Question 10:
(5, 10)

Question 11:
The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.

Question 12:
The total cost of 2 candies is $6.

Question 13:
Draw a graph that joins the points (100, 135) and (500, 375) and has a slope = 1.67

Question 14:
y = −6x − 15

Question 15:
{y | −4 ≤ y < ∞}

Feel free to ask if you have any questions or need further clarification!