Question

What is the average rate of change of f(x), represented by the table of values, over the interval [-3, 4]? x f(x) -6 27 -3 6 -1 2 0 3 1 6 4 27 A. -6 B. -3 C. 3 D. 6 E. 21

Answer 1

Answer:

The correct option will be:  C.  3

Step-by-step explanation:

The given table is..........

$x :$      -6      -3      -1      0      1      4

$f(x) :$  27     6      2      3      6     27

The formula for average rate of change is:   $\frac{f(b)-f(a)}{b-a}$ , where $[a,b]$ is the given interval.

Here the interval is [-3, 4]. So,  $a=-3$ and $b=4$

Now, plugging the values of $a$ and $b$ into the above formula, we will get........

$\frac{f(4)-f(-3)}{4-(-3)}$

From the given table, we will get  $f(4)=27$ and $f(-3)=6$

So, the average rate of change will be:  $\frac{27-6}{4-(-3)}= \frac{21}{7}=3$