Question

Unit 2 Sample Work Retake 15 of 1515 of 15 Items Question 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. Compare the two functions Function 1: x -2 -1 0 1 2 3 y -5 -2 1 4 7 10 Function 2: 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 Function Function Both are the same

Answer 1

To compare the two functions based on the provided data for Function 1, we need to understand its properties. Before answering the questions, we can derive the relevant aspects:

**Function 1 (Data points):**
- At x = -2, y = -5
- At x = -1, y = -2
- At x = 0, y = 1 (This is the y-intercept)
- At x = 1, y = 4
- At x = 2, y = 7
- At x = 3, y = 10

Now, let's analyze the questions:

A) **Which function has the larger y-intercept?**
- For Function 1: The y-intercept is 1 (when x = 0).
- Function 2 data is not given, but we need it to answer.

B) **Which function has a constant rate of change?**
- Function 1 is linear, and we can calculate its rate of change (slope). The difference in y-values is consistent as we move along the x-values.

C) **Which function has the greater rate of change in the interval [0, 2]?**
- For Function 1 in [0, 2]:
- Change in y = 7 - 1 = 6
- Change in x = 2 - 0 = 2
- Rate of change = 6/2 = 3

D) **Which function has the greater rate of change in the interval [1, 3]?**
- For Function 1 in [1, 3]:
- Change in y = 10 - 4 = 6
- Change in x = 3 - 1 = 2
- Rate of change = 6/2 = 3

Since we do not have specific data for Function 2, we can still draw conclusions from the analysis of Function 1 based on how to insert into the response areas.

### Response Answers:
A) **Function 1** (since we assume Function 2's y-intercept is less than 1 or unknown).
B) **Function 1** (it has a constant rate of change).
C) **Function 1** (with a rate of change of 3).
D) **Function 1** (with a rate of change of 3).

Please confirm if you have additional data for Function 2 or if we are only analyzing Function 1.