Question

1. Hannah states that this table of values represents the function f(x) = 3x − 4. Which statement explains why she is correct or incorrect?
A) She is correct, because the slope is −3, and the graph of the equation includes the point (−4, 0).
B) She is correct, because the constant rate of change is −3, and the graph of the equation includes the point (0, −4).
C) She is incorrect, because the constant rate of change is −9, and the y-intercept is −3.
D) She is incorrect because the table does not represent a linear function.

2. Find f(-10).
f(x) = 7x - 5
A) -75
B) -65
C) 65
D) 90

3.The graph shows the amount that Miracle Maid Service charges to clean a house. They charge a flat house visit fee plus an additional cost per room to clean a house. How much do they charge per room?
A) $30
B) $20
C) $10
D) $5

Answer 1

                                          Question # 1 Solution

Step-by-step Explanation:

Considering the function

$f(x) = 3x-4$

Option A) She is correct, because the slope is −3, and the graph of the equation includes the point (−4, 0)

Answer: She is not correct as the slope is 3 if we compare this equation with the slop intercept form which is $y=mx+c$.

Also, the graph of the equation does not include the point (−4, 0) as when when we put x=-4, the value of y will be -16. Which would be the point (-4, -16).

B) She is correct, because the constant rate of change is −3, and the graph of the equation includes the point (0, −4).

Answer: Though she is correct in saying that the graph of the equation includes the point (−4, 0) as the equation satisfies the equation, but she is not correct about the constant rate of change being -3, as the constant rate of change is 3 as the slope is 3 which is positive if we compare this equation with the slop intercept form which is $y=mx+c$.

C) She is incorrect, because the constant rate of change is −9, and the y-intercept is −3.

Answer: She is incorrect as the constant rate of change is not -9 as the slope of $f(x) = 3x-4$ is 3 if we compare this equation with the slop intercept form which is $y=mx+c$, also the y-intercept being -3 is also not correct as the y-intercept is -4, as shown in attached figure.

D) She is incorrect because the table does not represent a linear function.

Answer: She is incorrect if she says the table does not represent a linear function, because $f(x) = 3x-4$ represents a straight line, which indicates that it is a linear function, as shown in attached figure a.

Please check attached figure a for this question.

                                          Question # 2 Solution

Step-by-step Explanation:

Considering the function

$f(x) = 7x - 5$

We have to find $f(-10)$

Putting $x = -10$ in $f(x) = 7x - 5$

As

$f(x) = 7x - 5$

$f(-10) = 7(-10) - 5$

$f(-10) = -70 - 5$

$f(-10) = -75$

Therefore, $f(-10) = -75$

                            Question # 3 Solution

Note: As you missed to add the graph, after a little research I found the graph and hence I am attaching the graph, and based on that graph I am answering your query which anyways would clear your concepts.

Please check attached figure b for this question.

Step-by-step Explanation:

• As it is clear from the graph in the attached figure b that the x-axis is displaying the number of rooms,
• whereas the y-axis is displaying the cost of "x" number of rooms

As the initial house visit fee hasn't yet contained any rooms. Thus, we must be observing at the $x = 0$ - also knows as y-intercept. Also, the graph is intercepting the y-axis midway between 20 and 40.

Thus, we can conclude that the initial house visit fee is $30.

Keywords: slope, point, point slope form, rate of change

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