What will be the average rate of change of the function [y = 16 – x2] between x = 3 and x = 4?

The correct option is -7.

To find the average rate of change of a function $y=f\left(x\right)$ between two values $x=a$ and $x=b$, we use the average rate of change formula:
$$\text{Average Rate of Change}=\frac{f\left(b\right)-f\left(a\right)}{b-a}$$

For the given function $f\left(x\right)=16-x^2$, we need to compute this value between $x=3$ (which is our $a$) and $x=4$ (which is our $b$).

Step 1: Calculate $f\left(a\right)$ at $x=3$
Substitute $x=3$ into the function:
$$f\left(3\right)=16-3^2$$
$$f\left(3\right)=16-9=7$$

Step 2: Calculate $f\left(b\right)$ at $x=4$
Substitute $x=4$ into the function:
$$f\left(4\right)=16-4^2$$
$$f\left(4\right)=16-16=0$$

Step 3: Calculate the average rate of change
Now, substitute the values we found into the formula:
$$\text{Average Rate of Change}=\frac{f\left(4\right)-f\left(3\right)}{4-3}$$
$$\text{Average Rate of Change}=\frac{0-7}{4-3}$$
$$\text{Average Rate of Change}=\frac{-7}{1}=-7$$

Thus, the average rate of change of the function between $x=3$ and $x=4$ is indeed $-7$.