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

Question

2 years ago

6

2 0 3 1 6 4 27 A. -6 B. -3 C. 3 D. 6 E. 21

1 answer:

USPshnik [31] · Answer 1 · 2022-03-02T22:00:19+03:00

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: $\frac{27-6}{4-(-3)}= \frac{21}{7}=3$