Let $f(x)=\frac{3 x-6}{x^{2}+8 x+15}=\frac{(3 x-6)}{(x+5)(x+3)}$
Find:
2) the $y$ intercept at the point
3) $x$ intercepts at the point(s)
4) Vertical asymptotes at $x=$
5) Horizontal asymptote at $y=$
Answer
Final Answer: The y-intercept of the function is at the point $(0, -\frac{2}{5})$. So, the y-intercept is \(\boxed{-\frac{2}{5}}\).
Step 1 ：Let $f(x)=\frac{3 x-6}{x^{2}+8 x+15}=\frac{(3 x-6)}{(x+5)(x+3)}$
Step 2 ：The y-intercept is the point where the graph of the function intersects the y-axis. This occurs when x = 0.
Step 3 ：Substitute x = 0 into the function and solve for y.
Step 4 ：$f = \frac{3*0 - 6}{((0 + 3)*(0 + 5))}$
Step 5 ：Calculate the value to get the y-intercept.
Step 6 ：Final Answer: The y-intercept of the function is at the point $(0, -\frac{2}{5})$. So, the y-intercept is \(\boxed{-\frac{2}{5}}\).
