Question

Compare the two functions.

Function 1:

x -2 -1 0 1 2 3
y -3 2 7 12 17 22


Function 2:





(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A) Which function has the larger y-intercept? Response area

B) Which function has a constant rate of change? Response area

C) Which function has the greater rate of change in the interval [0, 2]? Response area

D) Which function has the greater rate of change in the interval [1, 3]? Response area

Answer 1

To compare the two functions, we'll start by determining the properties such as the y-intercept, rate of change, and specific intervals as described in the questions A-D.

For **Function 1**, we have the following data points:
- When \( x = 0 \), \( y = 7 \) (this is the y-intercept).
- The differences between consecutive y values can be calculated to determine the rate of change.

### Rates of Change for Function 1:
- From \( -2 \) to \( -1 \): Change in y = \( 2 - (-3) = 5 \)
- From \( -1 \) to \( 0 \): Change in y = \( 7 - 2 = 5 \)
- From \( 0 \) to \( 1 \): Change in y = \( 12 - 7 = 5 \)
- From \( 1 \) to \( 2 \): Change in y = \( 17 - 12 = 5 \)
- From \( 2 \) to \( 3 \): Change in y = \( 22 - 17 = 5 \)

The **rate of change** is constant and equal to \( 5 \).

### Now for **Function 2**, let's assume it consists of the same generated points because those were not provided. If it is different, note its properties separately.

Assuming the context allows for hypothetical linear behavior or uses the same incremental values, I will approach as if it also maintains a consistent interval unless stated otherwise.

### Answers to the questions:
A) **Which function has the larger y-intercept?**
- Function 1 has a y-intercept of \( 7 \), while Function 2 would need to be defined or calculated if it differs. Assuming it is lesser or similar to \( 7 \) based on standard comparisons, we stated Function 1.

Answer: **Function 1**.

B) **Which function has a constant rate of change?**
- Function 1 displays a constant rate of change of \( 5 \).

Answer: **Function 1**.

C) **Which function has the greater rate of change in the interval [0, 2]?**
- For Function 1, the change from \( y = 7 \) to \( y = 17 \) (change of \( 10 \)) over the interval of \( [0, 2] \) gives a rate of change of: \(\frac{10}{2-0} = 5\).
- Function 2's rate of change would depend on direct values, but assuming a linear relationship might equal \( 5 \) or differ.

Assuming equal or lower performance:
Answer: **Function 1**.

D) **Which function has the greater rate of change in the interval [1, 3]?**
- For Function 1, the change from \( y = 12 \) to \( y = 22 \) (change of \( 10 \)) leads to a rate of change of \(\frac{10}{3-1} = 5\).
- Again, Function 2 would need specific values based on its formulation for clarity.

Assuming no values make function 2 stand out:
Answer: **Function 1**.

In summary:
- A) **Function 1**
- B) **Function 1**
- C) **Function 1**
- D) **Function 1**

You can adjust the responses for Function 2 based on any specific data it provided that contrasts from these conclusions.