question 8\nfind the average rate of change of ( f(x)=x^{2}-5 ) from ( x=-3 ) to ( x = 2 ).\n\nquestion…

question 8\nfind the average rate of change of ( f(x)=x^{2}-5 ) from ( x=-3 ) to ( x = 2 ).\n\nquestion 9\ngraph ( h(x)=x^{2} ) on the cartesian plane.\nchoose the name of the toolkit function you graphed. quadratic

question 8\nfind the average rate of change of ( f(x)=x^{2}-5 ) from ( x=-3 ) to ( x = 2 ).\n\nquestion 9\ngraph ( h(x)=x^{2} ) on the cartesian plane.\nchoose the name of the toolkit function you graphed. quadratic

Answer

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}). [ \begin{align*} \frac{-1-4}{2 + 3}&=\frac{-5}{5}\ &=-1 \end{align*} ]

Answer:

(-1)