Question

find average rate of change from table
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given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval $4 \leq x \leq 8$.
answer attempt 1 out of 2
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Explanation:

Step1: Identify endpoints of interval

From the table, at $x=4$, $f(4)=7$; at $x=8$, $f(8)=43$.

Step2: Apply average rate formula

The formula for average rate of change over $[a,b]$ is $\frac{f(b)-f(a)}{b-a}$. Substitute $a=4$, $b=8$, $f(a)=7$, $f(b)=43$:
$\frac{43 - 7}{8 - 4}$

Step3: Calculate numerator and denominator

$43-7=36$, $8-4=4$

Step4: Simplify the fraction

$\frac{36}{4}=9$

Answer:

9