for the function f(x)= -3x + 1, evaluate and simplify the difference quotient.

Explanation:

Step1: Recall difference - quotient formula

The difference - quotient formula for a function $y = f(x)$ is $\frac{f(x + h)-f(x)}{h}$, where $h\neq0$.

Step2: Find $f(x + h)$

Given $f(x)=-3x + 1$, then $f(x + h)=-3(x + h)+1=-3x-3h + 1$.

Step3: Substitute $f(x + h)$ and $f(x)$ into the difference - quotient formula

$\frac{f(x + h)-f(x)}{h}=\frac{(-3x-3h + 1)-(-3x + 1)}{h}$.

Step4: Simplify the numerator

$(-3x-3h + 1)-(-3x + 1)=-3x-3h + 1 + 3x-1=-3h$.

Step5: Simplify the fraction

$\frac{-3h}{h}=-3$.

Answer:

$-3$