Question

find the vertical and horizontal asymtotes, domain, range, holes, and graph it, list the points as well!!

Answer 1

SOLUTION:

The vertical asymptotes are the lines x=2 or x= -2

The horizontal asymptote is when y = 0

Holes: There are no holes

Domain:

$\begin{gathered} \lbrack-\infty\text{ }

Range:

[tex]\begin{gathered} \lbrack-\infty

[tex]\begin{gathered} \frac{2}{x^2-4^{}}\text{ = }\frac{2}{(\times-2)(x+2)} \\ x\text{ - 2 = 0} \\ x\text{ =2} \\ X\text{ + 2 =0} \\ X\text{ = -2} \\ vertical\text{ }asymptotes \end{gathered}$

For the horizontal asymptotes, since the degree of the numerator is less than that of the denominator, then y=0 is the horizontal asymptotes.