Use the table to answer the question.

To determine which function corresponds to the given input-output table, we can evaluate each provided function with the given values of \( x \) and check if the outputs match the outputs in the table.

Table Values:

• When \( x = -2 \), \( f(x) = -11 \)
• When \( x = -1 \), \( f(x) = -2 \)
• When \( x = 0 \), \( f(x) = 1 \)

Let's evaluate each function:

1. f(x) = 3x + 1

   • \( f(-2) = 3(-2) + 1 = -6 + 1 = -5 \) (not -11)
   • \( f(-1) = 3(-1) + 1 = -3 + 1 = -2 \) (matches)
   • \( f(0) = 3(0) + 1 = 1 \) (matches)

   Since \( f(-2) \) does not match, it cannot be this function.

2. f(x) = 6x + 1

   • \( f(-2) = 6(-2) + 1 = -12 + 1 = -11 \) (matches)
   • \( f(-1) = 6(-1) + 1 = -6 + 1 = -5 \) (not -2)
   • \( f(0) = 6(0) + 1 = 1 \) (matches)

   Since \( f(-1) \) does not match, it cannot be this function.

3. f(x) = -3x^2 + 1

   • \( f(-2) = -3(-2)^2 + 1 = -3(4) + 1 = -12 + 1 = -11 \) (matches)
   • \( f(-1) = -3(-1)^2 + 1 = -3(1) + 1 = -3 + 1 = -2 \) (matches)
   • \( f(0) = -3(0)^2 + 1 = -3(0) + 1 = 0 + 1 = 1 \) (matches)

   All values match, so this is a candidate.

4. f(x) = 3x^2 + 1

   • \( f(-2) = 3(-2)^2 + 1 = 3(4) + 1 = 12 + 1 = 13 \) (not -11)
   • \( f(-1) = 3(-1)^2 + 1 = 3(1) + 1 = 3 + 1 = 4 \) (not -2)
   • \( f(0) = 3(0)^2 + 1 = 3(0) + 1 = 0 + 1 = 1 \) (matches)

   Since \( f(-2) \) and \( f(-1) \) do not match, it cannot be this function.

Conclusion:

The function that matches all values in the table is:

f(x) = -3x² + 1

What are the correct coordinates for the function g(h)=−6h2−2h+h
with inputs of −8
, −6
, −4
, −2
, and 0?(1 point)
Responses

(−376,−8)
, (−210,−6)
, (−92,−4)
, (−30,−2)
, (0,0)
left parenthesis negative 376 comma negative 8 right parenthesis , left parenthesis negative 210 comma negative 6 right parenthesis , left parenthesis negative 92 comma negative 4 right parenthesis , left parenthesis negative 30 comma negative 2 right parenthesis , left parenthesis 0 comma 0 right parenthesis

(−8,−104)
, (−6,78)
, (−4,52)
, (−2,26)
, (0,0)
left parenthesis negative 8 comma negative 104 right parenthesis , left parenthesis negative 6 comma 78 right parenthesis , left parenthesis negative 4 comma 52 right parenthesis , left parenthesis negative 2 comma 26 right parenthesis , left parenthesis 0 comma 0 right parenthesis

(−8,−376)
, (−6,−210)
, (−4,−92)
, (−2,−22)
, (0,0)
left parenthesis negative 8 comma negative 376 right parenthesis , left parenthesis negative 6 comma negative 210 right parenthesis , left parenthesis negative 4 comma negative 92 right parenthesis , left parenthesis negative 2 comma negative 22 right parenthesis , left parenthesis 0 comma 0 right parenthesis

(−8,−360)
, (−6,−198)
, (−4,−84)
, (−2,−6)
, (0,0)

To determine the correct coordinates for the function \( g(h) = -6h^2 - 2h + h = -6h^2 - h \) for the specified inputs, we will calculate the output of the function for each input value: \(-8\), \(-6\), \(-4\), \(-2\), and \(0\).

Function:

\[ g(h) = -6h^2 - h \]

Calculating for each input:

1. For \( h = -8 \): \[ g(-8) = -6(-8)^2 - (-8) = -6(64) + 8 = -384 + 8 = -376 \] So, the point is \((-8, -376)\).

2. For \( h = -6 \): \[ g(-6) = -6(-6)^2 - (-6) = -6(36) + 6 = -216 + 6 = -210 \] So, the point is \((-6, -210)\).

3. For \( h = -4 \): \[ g(-4) = -6(-4)^2 - (-4) = -6(16) + 4 = -96 + 4 = -92 \] So, the point is \((-4, -92)\).

4. For \( h = -2 \): \[ g(-2) = -6(-2)^2 - (-2) = -6(4) + 2 = -24 + 2 = -22 \] So, the point is \((-2, -22)\).

5. For \( h = 0 \): \[ g(0) = -6(0)^2 - (0) = 0 \] So, the point is (0, 0).

Summary of Points:

The coordinates calculated are:

• \( (-8, -376) \)
• \( (-6, -210) \)
• \( (-4, -92) \)
• \( (-2, -22) \)
• \( (0, 0) \)

Final Answer

The correct response from the options provided is: \[ (-8, -376), (-6, -210), (-4, -92), (-2, -22), (0, 0) \]

So the third option: \[ (-8, -376), (-6, -210), (-4, -92), (-2, -22), (0, 0) \] is the correct set of coordinates.

Use the table to answer the question.

Input
(Boxes) Output
(Cost)
1 2.25
2 4.50
3 6.75
4 9.00
How can this function be represented algebraically?

(1 point)
Responses

y=−2.25x
y equals negative 2.25 x

y=x−2.25
y equals x minus 2.25

y=2.25x
y equals 2.25 x

y=x+2.25

To represent the function algebraically based on the given input-output table, we need to observe the pattern in the cost as the number of boxes increases.

Given Data:

• For 1 box, the cost is 2.25
• For 2 boxes, the cost is 4.50
• For 3 boxes, the cost is 6.75
• For 4 boxes, the cost is 9.00

Observations:

It seems that the cost increases as a multiple of the number of boxes:

• The cost for 1 box (2.25) can be expressed as \(2.25 \times 1\).
• The cost for 2 boxes can be expressed as \(2.25 \times 2\).
• The cost for 3 boxes can be expressed as \(2.25 \times 3\).
• The cost for 4 boxes can be expressed as \(2.25 \times 4\).

General Representation:

From these observations, we can see that the relationship can be expressed as: \[ \text{Cost} = 2.25 \times \text{Number of Boxes} \]

In terms of variables, if we let \(y\) be the cost and \(x\) be the number of boxes, we can write the equation as: \[ y = 2.25x \]

Conclusion:

The correct algebraic representation of the function based on the given table is: \[ y = 2.25x \]

Therefore, the response is: y = 2.25x.

Sariyah makes $8 per hour at her part-time job and works anywhere from 0 to 20 hours per week. She wants to graph her earnings. What would be a reasonable scale for the y-axis?(1 point)
Responses

100 to 200
100 to 200

0 to 8
0 to 8

0 to 20
0 to 20

0 to 200

To determine a reasonable scale for the y-axis representing Sariyah's earnings from her part-time job, we can calculate her potential earnings based on the given rate of pay and maximum hours worked.

Earnings Calculation

Sariyah earns $8 per hour and works between 0 and 20 hours per week. The calculation for her maximum earnings per week is: \[ \text{Maximum Earnings} = \text{Hourly Wage} \times \text{Maximum Hours} = 8 , \text{dollars/hour} \times 20 , \text{hours} = 160 , \text{dollars} \]

Reasonable Scale for the Y-axis

Given that her maximum earnings are $160, a suitable scale for the y-axis should ideally encompass this range.

• Option 1: 100 to 200 - This would work because it includes the maximum earnings, but it might not effectively show earnings ranging from $0 to $160.

• Option 2: 0 to 8 - This is too low since it only shows earnings for 1 hour of work, which is just $8.

• Option 3: 0 to 20 - This is also too low, as it does not account for earnings and only represents hours of work.

• Option 4: 0 to 200 - This is appropriate because it provides enough range to cover her potential earnings from $0 to $160 while remaining sufficiently open-ended if her hours increase in the future.

Conclusion

The most reasonable scale for the y-axis displaying Sariyah's earnings is: 0 to 200.

A teacher in Colorado receives an annual salary increase of $1,500 each year they continue to work at a school within a district. If Mr. Brown has an initial salary of $40,000, using the function s=1,500y+40,000
, where s is the total salary and y is the time in years, which of the following points on the graph represent how much Mr. Brown will make for teaching 3, 4, and 5 years in the district?(1 point)
Responses

(44,500,3)
, (46,000,4)
, and (47,500,5)
left parenthesis 44,500 comma 3 right parenthesis , left parenthesis 46,000 comma 4 right parenthesis , and left parenthesis 47,500 comma 5 right parenthesis

(3,4,500)
, (4,6,000)
, and (5,7,500)
left parenthesis 3 comma 4,500 right parenthesis , left parenthesis 4 comma 6,000 right parenthesis , and left parenthesis 5 comma 7,500 right parenthesis

(3,44,500)
, (4,46,000)
, and (5,47,500)
left parenthesis 3 comma 44,500 right parenthesis , left parenthesis 4 comma 46,000 right parenthesis , and left parenthesis 5 comma 47,500 right parenthesis

(−3,44,500)
, (−4,46,000)
, and (−5,47,500)

To determine how much Mr. Brown will make for teaching 3, 4, and 5 years in the district using the given function \( s = 1500y + 40000 \), where \( s \) is the total salary and \( y \) is the time in years, we can substitute the values of \( y \) into the function for each specified year.

Salary Calculations:

1. For \( y = 3 \) (3 years): \[ s = 1500(3) + 40000 = 4500 + 40000 = 44400 \]

2. For \( y = 4 \) (4 years): \[ s = 1500(4) + 40000 = 6000 + 40000 = 46000 \]

3. For \( y = 5 \) (5 years): \[ s = 1500(5) + 40000 = 7500 + 40000 = 47500 \]

Final Results:

• Mr. Brown's salary after 3 years will be $44,500.
• Mr. Brown's salary after 4 years will be $46,000.
• Mr. Brown's salary after 5 years will be $47,500.

Points Representation:

Thus, the points corresponding to the salaries after teaching 3, 4, and 5 years are:

• \((3, 44,500)\)
• \((4, 46,000)\)
• \((5, 47,500)\)

Conclusion

The correct response is: \[ (3, 44,500), (4, 46,000), (5, 47,500) \]

Thus, the third option: (3, 44,500), (4, 46,000), and (5, 47,500) is the correct and final answer.

Use the image to answer the question.

A line with an arrow at the top is plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Hours, and the y-axis is labeled Amount in Dollars.

Jasper is moving across town. His rental truck has a flat fee of $25 and an hourly charge of $15. The graph illustrates what he will pay. Interpret the graph. What is the rate of change?

(1 point)
Responses

25
25

−15
negative 15

15
15

40

To analyze the situation and determine the rate of change, we can break down the components described in the question:

Given Information:

1. Flat Fee: Jasper has a flat fee of $25 for the rental truck.
2. Hourly Charge: Additionally, there is an hourly charge of $15.

Interpretation of the Graph:

• The x-axis represents the number of hours Jasper rents the truck.
• The y-axis represents the total amount in dollars he will pay.

Calculation of Total Cost:

The total cost can be expressed as: \[ \text{Total Cost} = \text{Flat Fee} + (\text{Hourly Charge} \times \text{Number of Hours}) \] This can be formulated as: \[ \text{Cost} = 25 + 15x \] where \( x \) is the number of hours Jasper rents the truck.

Rate of Change:

The rate of change in this context refers to how much the total cost increases for each additional hour Jasper rents the truck. This is represented by the slope of the line on the graph.

Since the hourly charge is $15, it indicates that for every additional hour he rents the truck, the total cost increases by $15. Thus, the rate of change is:

\[ \text{Rate of Change} = 15 \]

Conclusion:

The correct response for the rate of change is: 15.