Match the characteristic on the left to the function that has the same on the right. (4 points)

Question

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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.