the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the…
the function $y = f(x)$ is graphed below. what is the average rate of change of the function $f(x)$ on the interval $-7 \\le x \\le -5$?
Answer
Explanation:
Step1: Identify function values at endpoints
From the graph, at $x = -7$, the $y$-value is $0$, so $f(-7) = 0$. At $x = -5$, the $y$-value is $12$, so $f(-5) = 12$.
Step2: Apply average rate of change formula
The average rate of change on $[a, b]$ is $\frac{f(b) - f(a)}{b - a}$. $$ \text{Rate} = \frac{f(-5) - f(-7)}{-5 - (-7)} $$
Step3: Calculate the numerical value
Substitute the identified values into the formula and simplify. $$ \text{Rate} = \frac{12 - 0}{-5 + 7} = \frac{12}{2} = 6 $$
Answer:
6