use the table below for f(x) to determine the average rate of change from f(-4) to f(0).\n| x | f(x) |\n| -5…

use the table below for f(x) to determine the average rate of change from f(-4) to f(0).\n| x | f(x) |\n| -5 | -67 |\n| -4 | -45 |\n| -3 | -27 |\n| -2 | -13 |\n| -1 | -3 |\n| 0 | 3 |\n| 1 | 5 |\n| 2 | 3 |

use the table below for f(x) to determine the average rate of change from f(-4) to f(0).\n| x | f(x) |\n| -5 | -67 |\n| -4 | -45 |\n| -3 | -27 |\n| -2 | -13 |\n| -1 | -3 |\n| 0 | 3 |\n| 1 | 5 |\n| 2 | 3 |

Answer

Explanation:

Step1: Identify the formula for average rate of change

The formula for 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, $a=-4$ and $b = 0$.

Step2: Find $f(-4)$ and $f(0)$ from the table

From the table, $f(-4)=-45$ and $f(0)=3$.

Step3: Substitute values into the formula

Substitute $f(-4)=-45$, $f(0)=3$, $a=-4$, and $b = 0$ into the formula $\frac{f(b)-f(a)}{b - a}$, we get $\frac{f(0)-f(-4)}{0-(-4)}=\frac{3-(-45)}{4}$.

Step4: Simplify the expression

First, simplify the numerator: $3-(-45)=3 + 45=48$. Then, $\frac{48}{4}=12$.

Answer:

$12$