QQuestionMathematics
QuestionMathematics
Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.
## Pairs
h(x) = x^2 + 2x - 6
A function, *f*, has an *x*-intercept at (2, 0) and a *y*-intercept at (0, - 10).
| *x* | 0 | 1 | 2 | 3 | 4 |
| --- | --- | --- | --- | --- | --- |
| *f(x)* | 4 | 0 | - 8 | - 20 | - 32 |
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Answer
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Step 1:I'll solve this step by step, carefully following the LaTeX formatting guidelines.
Step 2:: Calculate the average rate of change for h(x) = x^2 + 2x - 6
- Average rate of change = $$\frac{2 - (-6)}{2 - 0} = \frac{8}{2} = 4
- h(0) = (0)^2 + 2(0) - 6 = - 6
Step 3:: Calculate the average rate of change for the table function
- Average rate of change = $$\frac{-8 - 4}{2 - 0} = \frac{-12}{2} = -6
- f(0) = 4
Step 4:: Analyze the remaining representations
- By comparing the average rates of change, we can match the functions to their respective values.
Final Answer
- h(x) = x^2 + 2x - 6 has an average rate of change of 4 - The table function has an average rate of change of - 6
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