Question

The function f(x) is represented by this table of values. x f(x) -4 -12 -3 -5 -2 0 -1 3 0 4 1 3 Match the average rates of change of f(x) with the corresponding intervals. 1 2 4 6 [-4, -2] arrowRight [-2, 1] arrowRight [-3, 1] arrowRight [-4, 0] arrowRight

Answer 1

Answer:

6 goes with [-4,-2]

1 goes with [-2,1]

2 goes with [-3,1]

4 goes with [-4,0]

Step-by-step explanation:

x     f(x)

-----------

-4    -12

-3     -5

-2      0

-1      3

0      4

1        3

Before I continue, you need to know what f(a) means. f(a) means find x=a and the value that corresponds to it is f(a).

That is f(-4)=-12 from row 1.

That is f(-3)=-5 from row 2.

That is f(-2)=0 from row 3.

That is f(-1)=3 from row 4.

That is f(0)=4 from row 5.

That is f(1)=3 from row 6.

Average rate of change on $[a,b]$ is given by the formula:

$\frac{f(b)-f(a)}{b-a}$ or you could use $\frac{f(a)-f(b)}{a-b}$.

So the average rate of change on [-4,-2] is given by

$\frac{f(-4)-f(-2)}{-4-(-2)}=\frac{-12-0}{-2}=6$

The average rate of change on [-2,1] is given by

$\frac{f(1)-f(-2)}{1-(-2)}=\frac{3-0}{3}=1$

The average rate of change on [-3,1] is given by

$\frac{f(1)-f(-3)}{1-(-3)}=\frac{3-(-5)}{4}=\frac{8}{4}=2$

The average rate of change on [-4,0] is given by

$\frac{f(0)-f(-4)}{0-(-4)}=\frac{4-(-12)}{4}=\frac{16}{4}=4$