To match the characteristics on the left with the corresponding functions on the right, we can analyze each one:
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First value of 6 - This would correspond to a function that gives the first term of a sequence equal to 6. The equation that matches this is an = 6 + 7(n − 1).
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Y-intercept of 7 - For the linear function to have a y-intercept of 7, it must pass through the point (0,7). However, none of the provided functions explicitly have the y-intercept of 7, but an = 6 + 7(n − 1) has it built into the sequence form, so we might infer that it leads to a related function.
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Rate of change (common difference) of -4 - This would correspond to a linear function with a slope of -4. Therefore, it matches with f(x) = −4x + 2.
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Rate of change (common difference) of 6 - This refers to an arithmetic sequence where each term increases by 6. The corresponding function is an = -4 + 6(n − 1).
Summarizing these correlations:
- First value of 6: an = 6 + 7(n − 1)
- Y-intercept of 7 (implicitly as first term): an = 6 + 7(n − 1)
- Rate of change of -4: f(x) = −4x + 2
- Rate of change of 6: an = -4 + 6(n − 1)
If we were to match them in a structured way, it looks like this:
- First value of 6: an = 6 + 7(n − 1)
- Y-intercept of 7: f(x) = −4x + 2 (based on existing sequences)
- Rate of change (common difference) of -4: f(x) = −4x + 2
- Rate of change (common difference) of 6: an = -4 + 6(n − 1)
Please apply these matches to your input fields accordingly.
3 answers