find the difference quotient for the function f(x)=7x + 5, and simplify it. the difference quotient is

Answer:

7

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 $f(x)=7x + 5$, then $f(x + h)=7(x + h)+5=7x+7h + 5$.

Step2: Substitute into the formula

$\frac{f(x + h)-f(x)}{h}=\frac{(7x + 7h+5)-(7x + 5)}{h}$.

Step3: Simplify the numerator

$(7x + 7h+5)-(7x + 5)=7x+7h + 5-7x - 5=7h$.

Step4: Simplify the fraction

$\frac{7h}{h}=7$ (since $h\neq0$).