Answer
The difference quotient for the provided function is $3$.
Work Step by Step
Consider the provided function: $f\left( x \right)=3x+7$.
Now, substitute $x=x+h$ in the above equation to find $f\left( x+h \right)$
That is,
$f\left( x+h \right)=3\left( x+h \right)+7$
Now, apply the difference quotient formula,
$\begin{align}
& \frac{f\left( x+h \right)-f\left( x \right)}{h}=\frac{3\left( x+h \right)+7-\left( 3x+7 \right)}{h} \\
& =\frac{3x+3h+7-3x-7}{h} \\
& =\frac{3h}{h} \\
& =3
\end{align}$
Hence, the difference quotient for the provided function is $3$.
