Question

What is the difference quotient of the function, g(a) = StartFraction 8 minus a Over 4 EndFraction?

Answer 1

Given:

The function is:

$g(a)=\dfrac{8-a}{4}$

To find:

The difference quotient of the function.

Solution:

Formula for difference quotient of the function f(x) is:

$DQ=\dfrac{f(x+h)-f(x)}{h}$

We have,

$g(a)=\dfrac{8-a}{4}$

The difference quotient of the function g(a) is:

$DQ=\dfrac{g(a+h)-g(a)}{h}$

$DQ=\dfrac{\dfrac{8-(a+h)}{4}-\dfrac{8-a}{4}}{h}$

$DQ=\dfrac{\dfrac{8-a-h-8+a}{4}}{h}$

$DQ=\dfrac{-h}{4h}$

$DQ=-\dfrac{1}{4}$

Therefore, the difference quotient of the given function is $-\dfrac{1}{4}$.