Answer
The difference quotient for the given function is $3$
Work Step by Step
$f(x)=3x+7$
Find the difference quotient $\dfrac{f(x+h)-f(x)}{h}$
Start by finding $f(x+h)$. Substitute $x$ by $x+h$ in $f(x)$ and simplify:
$f(x+h)=3(x+h)+7=3x+3h+7$
Substitute the known values into the formula for the difference quotient and simplify:
$\dfrac{f(x+h)-f(x)}{h}=\dfrac{3x+3h+7-(3x+7)}{h}=...$
$...=\dfrac{3x+3h+7-3x-7}{h}=\dfrac{3h}{h}=3$
The difference quotient for the given function is $3$
