Question

Find the domain, range, x and y intercepts, and horizontal and vertical asymptotes of
f(x) = 2/x^2-2x-3

Answer 1

\[f(x)=\frac{2}{x^2-2x-3}\]The restrictions on the domain will be any values of x where the denominator is zero. In other words, you have to solve:\[x^2-2x-3=0\]Can you do this?

Answer 2

Yes, the answer would be x=3 or x=1

Answer 3

close. x=3 or x=-1

Answer 4

so when x is 3 or -1, the denominator is zero. We cannot divide by zero, so these values of x are not allowed. x can be any other real number other than these two. We write:\[D={x: x \in \mathbb{R}, x \neq3,x \neq -1}\]

Answer 5

Do you know any calculus?

Answer 6

Ok, a vertical asymptote looks like this: