Question 1 (1 point)
What is the average rate of change for the function $f(x)=x^{2}+x-7$ over the interval $-2 \leq x \leq 0$ ?

Answer

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Answer

Final Answer: The average rate of change for the function $f(x)=x^{2}+x-7$ over the interval $-2 \leq x \leq 0$ is $\boxed{-1.0}$.

Steps

Step 1 ：Given the function $f(x) = x^{2} + x - 7$ and the interval $[-2, 0]$.

Step 2 ：We need to calculate $f(0)$ and $f(-2)$.

Step 3 ：Substitute $x = 0$ into the function, we get $f(0) = 0^{2} + 0 - 7 = -7$.

Step 4 ：Substitute $x = -2$ into the function, we get $f(-2) = (-2)^{2} + (-2) - 7 = -3$.

Step 5 ：The average rate of change of a function over an interval $[a, b]$ is given by the formula: $\frac{f(b) - f(a)}{b - a}$.

Step 6 ：Substitute $a = -2$, $b = 0$, $f(a) = -3$, and $f(b) = -7$ into the formula, we get $\frac{-7 - (-3)}{0 - (-2)} = -1.0$.

Step 7 ：Final Answer: The average rate of change for the function $f(x)=x^{2}+x-7$ over the interval $-2 \leq x \leq 0$ is $\boxed{-1.0}$.