Exercises: Calculate and Interpret the Average Rate of Change of a Function

A line passes through $(1, 3)$ and $(4, 12)$. What is the slope of the line?

If $f(x) = x^2 + 3x$, what is $f(2)$?

For a linear function $f(x) = 5x - 2$, which statement about slope is true?

Let $f(x) = 3x + 7$. Find the average rate of change of $f$ over the interval $[1, 5]$.

Let $g(x) = x^2$. Find the average rate of change of $g$ over the interval $[2, 5]$.

The table below shows values of a function $h$.

Average rate of change from $x = 0$ to $x = 6$: $\dfrac{h(6) - h(0)}{6 - 0} = \dfrac{\underline{\hspace{5em}} - \underline{\hspace{5em}}}{\hspace{0.2em}\fbox{\phantom{000000}}\hspace{0.2em}} = \underline{\hspace{5em}}$.

Let $p(t) = -16t^2 + 64t + 4$. Find the average rate of change of $p$ from $t = 1$ to $t = 3$.

Let $f(x) = \sqrt{x}$. Find the average rate of change of $f$ over the interval $[4, 16]$.