Fine the difference quote for the function $$ f(x)=3 x+5 $$. Simplify your answer as much as possible. $$ \frac{f(x+h)-f(x)}{h}= $$

Question

UpStudy AI · Accepted Answer

The difference quotient is given by

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

For the function $$ f(x)=3x+5 $$, we first compute $$ f(x+h) $$:

$$
f(x+h)=3(x+h)+5=3x+3h+5.
$$

Now, subtract $$ f(x) $$:

$$
f(x+h)-f(x)= (3x+3h+5)-(3x+5)=3h.
$$

Thus, the difference quotient simplifies to

$$
\frac{3h}{h}=3.
$$
The difference quotient simplifies to 3.

Fine the difference quote for the function \( f(x)=3 x+5 \). Simplify your answer as much as possible. \( \frac{f(x+h)-f(x)}{h}= \)