Question 1(Multiple Choice Worth 1 points)
(02.05 MC)
Given the function f(x) = 6x + 1 and the linear function g(x), which function has a greater slope?
positive linear function increasing through 2 comma 3 and 3 comma 7
a. f(x) has a greater slope.
b. g(x) has a greater slope.
c. The slopes of f(x) and g(x) are the same.
d. The slope of g(x) is undefined.
Question 2(Multiple Choice Worth 1 points)
(02.05 MC)
What are the vertex and range of y = |x + 1| + 3?
a. (0, 4); −∞ < y < ∞
b. (0, 4); 3 ≤ y < ∞
c. (−1, 3); −∞ < y < ∞
d. (−1, 3); 3 ≤ y < ∞
Question 3(Multiple Choice Worth 1 points)
(02.05 MC)
Graph g(x), where f(x) = 4x − 2 and g(x) = f(x + 1).
a. a line labeled g of x that passes through points 0, negative 2 and 1, 2
b. a line labeled g of x that passes through points 0, negative 3 and 1, 1
c. a line labeled g of x that passes through points negative 1, negative 2 and 0, 2
d. a line labeled g of x that passes through points 0, negative 1 and 1, 3
Question 4(Multiple Choice Worth 1 points)
(02.05 MC)
Given f(x) = 2x − 3 and g(x) = f(3x), which table represents g(x)?
x g(x)
1 −3
2 3
3 9
x g(x)
1 −1
2 1
3 3
x g(x)
1 3
2 6
3 9
x g(x)
1 3
2 9
3 15
Question 5(Multiple Choice Worth 1 points)
(02.05 MC)
If the parent function f(x) = |x| is transformed to g(x) = |x + 5|, what transformation occurs from f(x) to g(x)?
a. The graph of f(x) is shifted upward to create g(x).
b. The graph of f(x) is shifted downward to create g(x).
c. The graph of f(x) is shifted to the right to create g(x).
d. The graph of f(x) is shifted to the left to create g(x).
Question 6(Multiple Choice Worth 1 points)
(02.05 MC)
Write the equation of a function whose parent function, f(x) = x + 8, is shifted 2 units to the right.
a. g(x) = x − 6
b. g(x) = x − 2
c. g(x) = x + 2
d. g(x) = x + 6
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
Graph g(x) = |x + 3|.
a. The graph shows an upward opening v-shaped graph with a vertex at negative 3 comma 0, which passes through negative 4 comma 1 and negative 2 comma 1.
b. The graph shows an upward opening v-shaped graph with a vertex at 3 comma 0, which passes through 2 comma 1 and 4 comma 1.
c. The graph shows an upward opening v-shaped graph with a vertex at 0 comma 3, which passes through negative 1 comma 4 and 1 comma 4.
d. The graph shows an upward opening v-shaped graph with a vertex at 0 comma negative 3, which passes through negative 1 comma negative 2 and 1 comma negative 2.
Question 8(Multiple Choice Worth 1 points)
(02.05 MC)
A state park charges $5 per car, plus $1 per person as an admission fee. The total charged for a car with x people is f(x) = x + 5. How will the graph of this function change if the per car charge is changed to $8 per car?
a. The line will shift vertically down by $3.
b. The line will shift vertically up by $3.
c. The line will shift vertically up by $8.
d. The line will shift vertically down by $8.
Question 9(Multiple Choice Worth 1 points)
(02.05 MC)
Given the function f(x) = 4x + 10 and g(x), which function has a greater slope?
x g(x)
2 5
4 7
6 9
a. f(x) has a greater slope.
b. g(x) has a greater slope.
c. The slopes of f(x) and g(x) are the same.
d. The slope of g(x) is undefined.
Question 10(Multiple Choice Worth 1 points)
(02.05 MC)
Choose the table that represents g(x) = 3⋅f(x) when f(x) = x − 1.
a. x g(x)
1 2
2 1
3 0
b. x g(x)
1 2
2 5
3 8
c. x g(x)
1 5
2 8
3 11
d. x g(x)
1 0
2 3
3 6
1. b. g(x) has a greater slope.
2. d. (−1, 3); 3 ≤ y < ∞
3. b. a line labeled g of x that passes through points 0, negative 3 and 1, 1
4. d. x g(x)
1 3
2 9
3 15
5. c. The graph of f(x) is shifted to the right to create g(x).
6. d. g(x) = x + 6
7. a. The graph shows an upward opening v-shaped graph with a vertex at negative 3 comma 0, which passes through negative 4 comma 1 and negative 2 comma 1.
8. b. The line will shift vertically up by $3.
9. a. f(x) has a greater slope.
10. c. x g(x)
1 2
2 6
3 9
Question 1(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, 6 and 6, 8. Graph of another line segment going through the 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 acceleration of the runner was 8 m/s2, and the runner stopped after 6 seconds.
The initial acceleration of the runner was 6 m/s2, and the runner stopped after 8 seconds.
The initial velocity of the runner was 8 m/s, and the runner stopped after 6 seconds.
The initial velocity of the runner was 6 m/s, and the runner stopped after 8 seconds.
Question 2(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 3(Multiple Choice Worth 1 points)
(02.04 MC)
Choose the equation that represents the graph.
graph of a line passing through points 0 comma 6 and 9 comma 0
y = −2x − 6
y = two thirdsx + 6
y = negative two thirdsx + 6
y = 2x + 6
Question 4(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 9
4 17
g(x) = 3x + 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 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 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 greater than the y-intercept of g(x).
Question 5(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 6(Multiple Choice Worth 1 points)
(02.02 LC)
If f(x) is the height, in cm, of a sunflower plant that is x days old, which of the following statements best describes the meaning of f(60) = 210?
The height of the sunflower plant is 60 cm when it is 210 days old.
The height of the sunflower plant is 210 cm when it is 60 days old.
The height of the sunflower plant is 210 cm when it is 3.5 days old.
The height of the sunflower plant is 60 cm when it is 3.5 days old.
Question 7(Multiple Choice Worth 1 points)
(02.02 MC)
Given the function f(x) = −5x2 + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values.
The value of f(1) cannot be compared to the value of f(2).
The value of f(2) is larger than the value of f(1).
The value of f(2) is smaller than the value of f(1).
The value of f(1) is the same as the value of f(2).
Question 8(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 9(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 3 of the recall, the manufacturer fixed 391 cars. In week 13, the manufacturer fixed 361 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) = 3x + 400
f(x) = 3x + 391
f(x) = −3x + 391
f(x) = −3x + 400
Question 10(Multiple Choice Worth 1 points)
(02.05 MC)
Determine the range of f(x) = |x + 5|.
{y | −∞ < y < ∞}
{y | −5 < y < ∞}
{y | 0 ≤ y < ∞}
{y | 5 ≤ y < ∞}
Question 11(Multiple Choice Worth 1 points)
(02.02 MC)
A fisherman's production is modeled by function f(x), where f(x) is the number of fish caught per outing and x is the number of people fishing on the boat. Choose the ordered pair that represents a possible domain and range of the function.
(nineteen thirds, 15)
(22, 65)
(twenty two fifths, forty three sevenths)
(10, one hundred elevenths)
Question 12(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 $120 for 100 megabytes of data and $95 for 50 megabytes of data. An equation can be written to show the relationship between the total megabytes of data 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 (100, 120) and (50, 95) and has a slope = 0.50
Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 2
Draw a graph that joins the points (120, 100) and (95, 50) and has a slope = 2
Draw a graph that joins the points (120, 100) and (95, 50) and has a slope = 0.50
Question 13(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 14(Multiple Choice Worth 1 points)
(02.03 HC)
The following table shows the distance from school as a function of time:
Time (in minutes)
x Distance (in meters)
f(x)
0 36
3 32
6 28
9 24
12 20
Find and interpret the meaning of the x-intercept in this scenario.
(36, 0); the distance away from the school
(27, 0); the time it takes to reach the school
(36, 0); the time it takes to reach the school
(27, 0); the distance away from the school
Question 15(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
1. c. The initial velocity of the runner was 8 m/s, and the runner stopped after 6 seconds.
2. b. The graph shifts 5 units down.
3. d. y = 2x + 13
4. b. 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).
5. b. Domain: −∞ < x < ∞; Range: − 4 ≤ y < ∞; x-intercept (2, 0)
6. b. The height of the sunflower plant is 210 cm when it is 60 days old.
7. b. The value of f(2) is larger than the value of f(1).
8. d. y = -6x + 9
9. c. f(x) = -3x + 400
10. b. {y | 0 ≤ y < ∞}
11. (nineteen thirds, 15)
12. a. Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50
13. a. y = (-1/3)x + 1
14. (36, 0); the time it takes to reach the school
15. a. Slope of Function B = 2 x Slope of Function A
Question 1: The function with a greater slope is the positive linear function that increases through the points (2,3) and (3,7). Therefore, the answer is b. g(x) has a greater slope.
Question 2: The vertex and range of the function y = |x + 1| + 3 are (-1, 3) and 3 ≤ y < ∞. Therefore, the answer is d. (-1, 3); 3 ≤ y < ∞.
Question 3: To graph g(x), we have g(x) = f(x + 1). The points on the graph of g(x) will be shifted one unit to the left compared to the points on the graph of f(x). Therefore, the answer is c. a line labeled g of x that passes through points negative 1, negative 2 and 0, 2.
Question 4: Given g(x) = f(3x), we substitute the values of x into f(x) and find the corresponding values of g(x). From the table, we can see that when x is 1, g(x) is 3, when x is 2, g(x) is 9, and when x is 3, g(x) is 15. Therefore, the answer is d. x g(x) 1 3 2 9 3 15.
Question 5: The function g(x) = |x + 5| is obtained from the parent function f(x) = |x| by shifting the graph 5 units to the left. Therefore, the answer is d. The graph of f(x) is shifted to the left to create g(x).
Question 6: To shift the parent function f(x) = x + 8 two units to the right, we subtract 2 from x. Therefore, the equation of the function is g(x) = x + 6. Therefore, the answer is d. g(x) = x + 6.
Question 7: The graph of g(x) = |x + 3| is an upward-opening V-shaped graph with a vertex at (-3, 0), which passes through (-4, 1) and (-2, 1). Therefore, the answer is a. The graph shows an upward opening v-shaped graph with a vertex at negative 3 comma 0, which passes through negative 4 comma 1 and negative 2 comma 1.
Question 8: If the per car charge is changed to $8, the equation for the new function will be f(x) = x + 8. The graph of this function will shift vertically up by $3. Therefore, the answer is c. The line will shift vertically up by $8.
Question 9: To determine which function has a greater slope, we compare the difference in y-values over the difference in x-values for each function. For f(x), the slope is 4. For g(x), the slope is (7-5)/(4-2) = 1. Therefore, the answer is a. f(x) has a greater slope.
Question 10: To find the values of g(x) when g(x) = 3*f(x), we multiply the corresponding values of f(x) by 3. From the table, we can see that when x is 1, g(x) is 3*1 = 3, when x is 2, g(x) is 3*1 = 3, and when x is 3, g(x) is 3*2 = 6. Therefore, the answer is d. x g(x) 1 0 2 3 3 6.
Question 1: To determine which function has a greater slope, we need to compare the coefficients of x in the two functions. The function f(x) has a coefficient of 6, while the given linear function g(x) does not have a specific equation given. Therefore, we cannot determine the slope of g(x) without more information. The correct answer is:
b. g(x) has a greater slope.
Question 2: To find the vertex of the given function y = |x + 1| + 3, we need to find the x-value that makes the expression inside the absolute value equal to zero. Setting x + 1 = 0, we find x = -1. Therefore, the vertex is (-1, 3).
The range of the function y = |x + 1| + 3 can be found by considering that the absolute value of any expression is always non-negative. So, the minimum value of an absolute value function is zero. Therefore, the range of this function is y ≥ 3.
The correct answer is:
d. (-1, 3); 3 ≤ y < ∞
Question 3: To graph g(x) using the given information, we need to substitute x + 1 for x in the function f(x) = 4x - 2.
g(x) = f(x + 1) = 4(x + 1) - 2 = 4x + 4 - 2 = 4x + 2
Therefore, the graph of g(x) is a line labeled g(x) that passes through the points (0, 2) and (1, 6).
The correct answer is:
b. a line labeled g(x) that passes through points 0, -3 and 1, 1
Question 4: To find the function g(x) = f(3x), we need to substitute 3x for x in the function f(x) = 2x - 3.
g(x) = f(3x) = 2(3x) - 3 = 6x - 3.
The correct table representing g(x) is:
x g(x)
1 3
2 9
3 15
The correct answer is:
d. x g(x)
1 3
2 9
3 15
Question 5: The function g(x) = |x + 5| is a transformation of the parent function f(x) = |x|. The transformation is a horizontal shift to the left by 5 units.
The correct answer is:
d. The graph of f(x) is shifted to the left to create g(x).
Question 6: To write the equation of a function that is a transformation of the parent function f(x) = x + 8, shifted 2 units to the right, we need to subtract 2 from x in the equation.
The correct answer is:
c. g(x) = x + 2
Question 7: The graph of g(x) = |x + 3| is an upward opening v-shaped graph with a vertex at (-3, 0). The graph passes through the points (-4, 1) and (-2, 1).
The correct answer is:
a. The graph shows an upward opening v-shaped graph with a vertex at (-3, 0), which passes through (-4, 1) and (-2, 1).
Question 8: The given function f(x) = x + 5 represents the total charged for a car with x people. To change the per car charge to $8, we need to change the constant term in the equation from 5 to 8.
The correct answer is:
c. The line will shift vertically up by $3.
Question 9: To determine which function has a greater slope, we need to compare the coefficients of x in the two functions. The function f(x) has a coefficient of 4, while the given table representing g(x) has different coefficients for different values of x. Therefore, we cannot determine the slope of g(x) without more information. The correct answer is:
a. f(x) has a greater slope.
Question 10: To find the table representing g(x) = 3⋅f(x), where f(x) = x - 1, we need to multiply the y-values in the table for f(x) by 3.
The correct table representing g(x) is:
x g(x)
1 2
2 3
3 6
The correct answer is:
d. x g(x)
1 0
2 3
3 6