for the function f(x)= -2x + 6, evaluate and simplify the difference quotient.
for the function f(x)= -2x + 6, evaluate and simplify the difference quotient.
Answer
Answer:
-2
Explanation:
Step1: Recall difference - quotient formula
The difference quotient of a function $f(x)$ is $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$. Given $f(x)=-2x + 6$, then $f(x + h)=-2(x + h)+6=-2x-2h + 6$.
Step2: Substitute into the formula
$\frac{f(x + h)-f(x)}{h}=\frac{(-2x-2h + 6)-(-2x + 6)}{h}$.
Step3: Simplify the numerator
$(-2x-2h + 6)-(-2x + 6)=-2x-2h + 6 + 2x-6=-2h$.
Step4: Simplify the quotient
$\frac{-2h}{h}=-2$ (since $h\neq0$).