Question

Let f(x) = 3 − x . Find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

Answer 1

Answer: on usatestprep the answer is c.

Explanation:

`(-1)/(√(a) +√(a+h) )`

Answer 2

The average rate of change of f(x) from x = a to x = a + h is -1

Explanation:

Average rate of the function f(x) over [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)`

Given the function:

`f(x) = 3-x`

At x=a

f(a) = 3-a

At x = a+h

then;

f(a+h) = 3-(a+h) = 3-a-h

Using the formula for average rate of function:

`A(x) = (f(x+h)-f(x))/(x+h-x)`

Substitute the given values we have;

`A(x) = (3-a-h-(3-a))/(x+h-x)`

Simplify:

`A(x) = (3-a-h-3+a)/(h)`

or

`A(x) = (-h)/(h) = -1`

Therefore, the average rate of change of f(x) from x = a to x = a + h is, -1