the table shows the values of a function $f(x)$. what is the average rate of change of $f(x)$ from $- 1$ to…
the table shows the values of a function $f(x)$. what is the average rate of change of $f(x)$ from $- 1$ to $1$?\n|$x$|$f(x)$|\n|----|----|\n|$-3$|$-3$|\n|$-2$|$-1$|\n|$-1$|$3$|\n|$0$|$11$|\n|$1$|$27$|\n|$2$|$59$|\nenter your answer in the box.
Answer
Explanation:
Step1: Recall average - rate - of - change formula
The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$. Here, $a=-1$, $b = 1$, $f(-1)=3$, and $f(1)=27$.
Step2: Substitute values into formula
$\frac{f(1)-f(-1)}{1-(-1)}=\frac{27 - 3}{1+1}$.
Step3: Simplify the expression
$\frac{24}{2}=12$.
Answer:
12