Question 3
Let $f(x)=\frac{3x-6}{x^2+8x+15}=\frac{(3x-6)}{(x+5)(x+3)}$
Find:
1) the domain in interval notation
Note: Use -oo for $-\mathrm{\infty }$, oo for $\mathrm{\infty }$, U for union.
2) the $y$ intercept at the point
3) $x$ intercepts at the point(s)
4) Vertical asymptotes at $x=$
5) Horizontal asymptote at $y=$

Step 1 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function. The only values that are not in the domain of this function are those that make the denominator equal to zero, because division by zero is undefined.

Step 2 ：We need to find the values of x that make the denominator equal to zero. The denominator of the function is $x^2+8x+15$.

Step 3 ：The solutions to the equation $x^2+8x+15=0$ are $x=-5$ and $x=-3$. These are the values that make the denominator of the function equal to zero, and thus are not in the domain of the function.

Step 4 ：Therefore, the domain of the function is all real numbers except $x=-5$ and $x=-3$. In interval notation, this is $(-\mathrm{\infty },-5)\cup (-5,-3)\cup (-3,\mathrm{\infty })$.

Step 5 ：Final Answer: The domain of the function in interval notation is $\boxed{{\displaystyle (-\mathrm{\infty },-5)\cup (-5,-3)\cup (-3,\mathrm{\infty })}}$.