Question

Compare the two functions.
function 1
x -1 0 1 2 4 5
y -1 3 7 11 19 23
function 2
graph shows a line passing through (0,2) (1,3) (2,5) (3,9) (4,17)
(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.
Which function has the larger y-intercept? Response area

Which function has a constant rate of change? Response area

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

Which function has the greater rate of change in the interval [2,4]? Response area

Answer 1

Let's analyze the two functions based on the provided information.

**Function 1:**
Values:
- x: -1, 0, 1, 2, 4, 5
- y: -1, 3, 7, 11, 19, 23

**Function 2:**
Points:
- (0, 2), (1, 3), (2, 5), (3, 9), (4, 17)

Now, let's answer each question:

1. **Which function has the larger y-intercept?**
- **Function 1:** The y-intercept (when x = 0) is 3.
- **Function 2:** The y-intercept (when x = 0) is 2.
- **Conclusion:** Function 1 has the larger y-intercept.

2. **Which function has a constant rate of change?**
- **Function 1:** The changes in y are not consistent; thus, it does not have a constant rate of change.
- **Function 2:** The differences in y-values for each x value are:
- From (0,2) to (1,3): +1
- From (1,3) to (2,5): +2
- From (2,5) to (3,9): +4
- From (3,9) to (4,17): +8
- The rate of change is not constant as well. (This was tested specifically through the number of increments.)
- **Conclusion:** Neither function has a constant rate of change.

3. **Which function has the greater rate of change in the interval [0,2]?**
- **Function 1:**
- At x = 0, y = 3; at x = 2, y = 11.
- The rate of change = (11 - 3) / (2 - 0) = 8 / 2 = 4.
- **Function 2:**
- At x = 0, y = 2; at x = 2, y = 5.
- The rate of change = (5 - 2) / (2 - 0) = 3 / 2 = 1.5.
- **Conclusion:** Function 1 has the greater rate of change in the interval [0, 2].

4. **Which function has the greater rate of change in the interval [2,4]?**
- **Function 1:**
- At x = 2, y = 11; at x = 4, y = 19.
- The rate of change = (19 - 11) / (4 - 2) = 8 / 2 = 4.
- **Function 2:**
- At x = 2, y = 5; at x = 4, y = 17.
- The rate of change = (17 - 5) / (4 - 2) = 12 / 2 = 6.
- **Conclusion:** Function 2 has the greater rate of change in the interval [2, 4].

### Summary of Responses:
1. **Larger y-intercept:** Function 1
2. **Constant rate of change:** Neither function
3. **Greater rate of change in [0,2]:** Function 1
4. **Greater rate of change in [2,4]:** Function 2