Question

✖️-101 2 3 f(✖️) -2-1 -1/2-1/4-1/8 -9/4 -7/12 12/7 7/12 Given the following table,fine the rate of change between f(-1) and f(2).

Answer 1

Answer: $\frac{7}{12}.$

Step-by-step explanation:

Given table:

X            f(X)

-1                -2

0                 -1

1                  $-\dfrac{1}{2}$

2                 $-\dfrac{1}{4}$

3                 $-\dfrac{1}{8}$

i.e. , f(-1) = -2

f(2) = $-\dfrac{1}{4}$

The rate of change between $f(a)$ and $f(b)=\dfrac{f(b)-f(a)}{b-a}$

Then, the rate of change between f(-1) and f(2) = $\dfrac{-\dfrac{1}{4}-(-2)}{2-(-1)}$

$=\dfrac{-\dfrac{1}{4}+2}{3}=\dfrac{\dfrac{-1+8}{4}}{3}\\\\=\dfrac{\dfrac{7}{4}}{3}\\\\=\dfrac{7}{12}$

Hence, the rate of change between f(-1) and f(2) is $\frac{7}{12}.$