Question 3 of 13, Step 1 of 1
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Correct
What is the average rate of change of $f(x)$ from $x_{1}=2$ to $x_{2}=6$ ? Please write your answer as an integer or simplified fraction.
\[
f(x)=-4 x+2
\]
Answer
Answer
The average rate of change of \(f(x)\) from \(x_{1}=2\) to \(x_{2}=6\) is \(\boxed{-4}\).
Step 1 ：The average rate of change of a function \(f(x)\) from \(x_{1}\) to \(x_{2}\) is given by the formula: \[\frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}\]
Step 2 ：Substitute \(x_{1}=2\) and \(x_{2}=6\) into the function \(f(x)=-4x+2\) and then use the formula to calculate the average rate of change.
Step 3 ：The function is a linear function with a slope of -4, so the average rate of change over any interval will be the same as the slope.
Step 4 ：The average rate of change of \(f(x)\) from \(x_{1}=2\) to \(x_{2}=6\) is \(\boxed{-4}\).
