Find all y-intercepts of the following function. Express your answer as a coordinate point in
simplest form.

Ask by Rojas Murphy. in the United States

Dec 09,2024

Question

Find all y-intercepts of the following function. Express your answer as a coordinate point in simplest form. $$ f(x)=\frac{x^{2}+14 x+48}{3 x+18} $$

UpStudy AI · Accepted Answer

To find the y-intercept of the function $$ f(x) = \frac{x^2 + 14x + 48}{3x + 18} $$, we need to evaluate the function at $$ x = 0 $$.

First, we substitute $$ x = 0 $$ into the function:

$$
f(0) = \frac{0^2 + 14(0) + 48}{3(0) + 18} = \frac{48}{18}
$$

Next, we simplify $$ \frac{48}{18} $$:

$$
\frac{48}{18} = \frac{48 \div 6}{18 \div 6} = \frac{8}{3}
$$

Thus, the y-intercept of the function is at the point $$ (0, \frac{8}{3}) $$.

Therefore, the y-intercept of the function is:

$$
\boxed{\left(0, \frac{8}{3}\right)}
$$
The y-intercept is at the point $$ (0, \frac{8}{3}) $$.

Find all y-intercepts of the following function. Express your answer as a coordinate point in
simplest form.