Question

question 8
find the average rate of change of ( f(x)=x^{2}-5 ) from ( x=-3 ) to ( x = 2 ).

question 9
graph ( h(x)=x^{2} ) on the cartesian plane.
choose the name of the toolkit function you graphed. quadratic

Explanation:

Step1: Recall 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, \(a=-3\), \(b = 2\), and \(f(x)=x^{2}-5\).

Step2: Calculate \(f(-3)\) and \(f(2)\)

• For \(x=-3\): \(f(-3)=(-3)^{2}-5=9 - 5=4\).
• For \(x = 2\): \(f(2)=2^{2}-5=4 - 5=-1\).

Step3: Substitute into the average - rate - of - change formula

\(\frac{f(2)-f(-3)}{2-(-3)}=\frac{-1 - 4}{2 + 3}\).

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Answer:

\(-1\)