Answer:
Average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.
Step-by-step explanation:
The formula for average rate of change of f(x) over [a,b] is
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The given function is
[tex]r(x)=x^2+2x-5[/tex]
[tex]r(0)=(0)^2+2(0)-5=-5[/tex]
[tex]r(3)=(3)^2+2(3)-5=10[/tex]
Now,
[tex]m_1=\dfrac{r(3)-r(0)}{3-0}[/tex]
[tex]m_1=\dfrac{10-(-5)}{3}=5[/tex]
From the graph it is clear that q(0)=-4 and q(3)=5.
[tex]m_2=\dfrac{q(3)-q(0)}{3-0}[/tex]
[tex]m_2=\dfrac{5-(-4)}{3}=3[/tex]
It is given that function p has as x-intercept at (3,0) and a y-intercept at (0,6). It menas p(0)=6 and p(3)=0.
[tex]m_3=\dfrac{p(3)-p(0)}{3-0}[/tex]
[tex]m_3=\dfrac{0-6}{3}=-2[/tex]
From the given table it is clear that s(0)=-13 and s(3)=5.
[tex]m_4=\dfrac{s(3)-s(0)}{3-0}[/tex]
[tex]m_4=\dfrac{5-(-13)}{3}=6[/tex]
Therefore, the average rate of change of functions r, q, p, s are 5, 3, -2 and 6 respectively.