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

Question

Function A

f(x) = 6x - 1

Function B

graph of line going through ordered pairs 1, 4 and negative 1, negative 2 and negative 2, negative 5

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 2(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 3(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) + 4?

The graph shifts 4 units up.
The graph shifts 4 units down.
The graph shifts 4 units left.
The graph shifts 4 units right.
Question 4(Multiple Choice Worth 1 points)
(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 5(Multiple Choice Worth 1 points)
(02.04 MC)

Write an equation of a line that is perpendicular to y = 4x + 8 and passes through (−8, 4).

y equals negative one-fourth times x minus 7
y equals negative one-fourth times x plus 2
y = 4x + 24
y = 4x + 36
Question 6(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 7(Multiple Choice Worth 1 points)
(02.04 MC)

Choose the equation that represents the line passing through the point (2, - 5) with a slope of −3.

y = −3x − 13
y = −3x + 11
y = −3x + 13
y = −3x + 1
Question 8(Multiple Choice Worth 1 points)
(02.02 MC)

A bakery's production is modeled by function f(x), where f(x) is the number of donuts made in a day and x is the number of bags of flour needed. Choose the ordered pair that represents a possible domain and range of the function.

(−1, 15)
(5, 92.75)
(10, 100)
(−5, 110.5)
Question 9(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 < ∞}
Question 10(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 2 of the recall, the manufacturer fixed 192 cars. In week 4, manufacturer fixed 184 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 at the mechanic.

f(x) = 4x + 200
f(x) = 2x + 192
f(x) = −4x + 200
f(x) = −2x + 192
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)
(02.05 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 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 $155 for 100 megabytes and $245 for 200 megabytes. 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 (155, 100) and (245, 200) and has a slope = 0.9
Draw a graph that joins the points (155, 100) and (245, 200) and has a slope = 1.1
Draw a graph that joins the points (100, 155) and (200, 245) and has a slope = 1.1
Draw a graph which joins the points (100, 155) and (200, 245) and has a slope = 0.9
Question 14(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 15(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)

Answer 1

Here are the answers to your questions:

Question 1: The equation for the slope of Function A (f(x) = 6x - 1) is 6. To find the slope of Function B from the points (1, 4) and (-1, -2), use the slope formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 4}{-1 - 1} = \frac{-6}{-2} = 3. \] So, the slopes are 6 for Function A and 3 for Function B. The correct comparison is: Slope of Function A = 2 x Slope of Function B.

Question 2: The statement that best describes the meaning of f(60) = 210 is: The height of the sunflower plant is 210 cm when it is 60 days old.

Question 3: The effect of replacing the graph of f(x) with the graph of f(x) + 4 is: The graph shifts 4 units up.

Question 4: To find the x-intercept from the water leaking table, we observe that the water decreases from 35 liters to 0:

1. The value at 0 minutes = 35 liters.
2. From the trend, it appears to take 7 minutes to reach 0 liters. Thus, the x-intercept is: (7, 0); the time it takes to empty the water in the pool.

Question 5: The slope of the perpendicular line to y = 4x + 8 is -1/4, and using point-slope form through the point (−8, 4), we derive: \[ y - 4 = -\frac{1}{4}(x + 8) \] So, the equation simplifies to: y = -\frac{1}{4}x + 2. Therefore, the correct equation is: y = -\frac{1}{4}x + 2.

Question 6: To find f(1) and f(2):

• f(1) = -5(1)^2 + 2(1) + 9 = 6
• f(2) = -5(2^2) + 2(2) + 9 = -5 * 4 + 4 + 9 = -20 + 4 + 9 = -7 Thus, the comparison is: The value of f(2) is smaller than the value of f(1).

Question 7: Using point-slope form: \[ y + 5 = -3(x - 2) \] Simplifying gives: \[ y = -3x + 6 - 5 \] \[ y = -3x + 1 \] Thus, the equation is: y = -3x + 1.

Question 8: Since the number of donuts cannot be negative:

• The ordered pair (−1, 15) is not valid.
• The others do not apply to the context, but (10, 100) indicates a clear non-negative number of bags to donuts relationship: (10, 100).

Question 9: The absolute function f(x) = |x| - 4 has a minimum of -4 when x = 0. Thus, the range is: {y | −4 ≤ y < ∞}.

Question 10: Using the points provided:

• 192 cars at week 2, and 184 cars at week 4: The slope = (184 - 192) / (4 - 2) = -8 / 2 = -4. Using point-slope at (2, 192): f(x) = -4(x - 2) + 192 simplifies to: f(x) = -4x + 200.

Question 11: For the velocity graph: The initial velocity is represented by the y-intercept, which is 2 m/s, and it reaches 0 m/s after 8 seconds: The initial velocity of the runner was 2 m/s, and the runner stopped after 8 seconds.

Question 12: From the table: The slope (change in y/change in x) is (4 - 1)/(2 - 0) = 3/2. In comparison, the slope of g(x) = 2. Thus: 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).

Question 13: Finding the slope between the points (100, 155) and (200, 245): The slope = (245 - 155) / (200 - 100) = 90 / 100 = 0.9. Thus: Draw a graph that joins the points (100, 155) and (200, 245) and has a slope = 0.9.

Question 14: From the points (-2, 0) & (0, -4), we find the slope: \( m = \frac{-4 - 0}{0 - (-2)} = \frac{-4}{2} = -2 \). Using point-slope: y = -2x - 4.

Question 15: For g(x) = -4x + 8:

• The domain is all real numbers.
• The range is all real numbers.
• The x-intercept is found by setting y = 0: \(0 = -4x + 8 \) gives \( x = 2\). So the answer is: Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0).

Let me know if you need any more assistance!