Question

The table shows the values of a function f(x).

Answer 1

Answer:

-4

Step-by-step explanation:

The average rate of change of a function f(x) between two points x = a and x=b is given by,

$f(x)=\frac{f(b)-f(a)}{b-a}$

This can be understood with a simpler example, the straight line.

In this case, the rate of change of the 'function' is given by the slope,

$m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$;                

$(x_{1},f(x_{1})),(x_{2},f(x_{2}))$ being two points on the straight line.

So, for the given problem,

a = -2

b = 2

Hence, average rate of change of $f(x)=\frac{f(2)-f(-2)}{2-(-2)} =\frac{9-25}{2+2} =\frac{-16}{4} =-4$

Answer 2

Answer:

-4

Step-by-step explanation:

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