Question

the graph of a function f is shown below. use the graph of the function to find its average rate of change from x = -5 to x = -3. simplify your answer as much as possible.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \(y = f(x)\) from \(x=a\) to \(x = b\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \(a=-5\) and \(b=-3\).

Step2: Identify the function values from the graph

From the graph, when \(x=-5\), \(y = f(-5)=-1\) (assuming the \(y\) - value at \(x = - 5\) based on the graph's scale). When \(x=-3\), \(y=f(-3)=1\) (assuming the \(y\) - value at \(x=-3\) based on the graph's scale).

Step3: Substitute into the formula

Substitute \(a=-5\), \(b = - 3\), \(f(a)=-1\), and \(f(b)=1\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{1-(-1)}{-3-(-5)}=\frac{1 + 1}{-3 + 5}\).

Step4: Simplify the expression

Simplify \(\frac{1 + 1}{-3 + 5}=\frac{2}{2}\).

Answer:

\(1\)