Question

Match the characteristic on the left to the function that has the same on the right. (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.
rate of change (common difference) of 6
first value of 6
rate of change (common difference) of -4
y-intercept of 7


an = -4+6(n-1)


f(x)=-4x+2


an=6+7(n-1)

Answer 1

Let's match the characteristics to the functions based on the provided information:

1. **Rate of change (common difference) of 6**: This matches the function \( a_n = 6 + 7(n-1) \) where 6 is the first value and the common difference is 6.

2. **First value of 6**: This matches \( a_n = 6 + 7(n-1) \) because when \( n = 1 \), \( a_1 = 6 \).

3. **Rate of change (common difference) of -4**: This matches the function \( a_n = -4 + 6(n - 1) \) because the common difference is -4.

4. **Y-intercept of 7**: This matches the function \( f(x) = -4x + 2 \) as it does not apply correctly here. This appears to be a misplacement.

However, based on the characters provided, here are the corrected matches:

1. Rate of change (common difference) of 6: **\( a_n = 6 + 7(n-1) \)**
2. First value of 6: **\( a_n = 6 + 7(n-1) \)**
3. Rate of change (common difference) of -4: **\( a_n = -4 + 6(n-1) \)**
4. Y-intercept of 7: **None of the provided functions correctly fit this**.

If it is placed incorrectly or misunderstood, please clarify so that I may assist further.