Question

I need to find the domain and range, the x and y intercepts and the horizontal and vertical asymptoteand then I need to graph it.

x^2+x-2/x^2-3x-4

Answer 1

domain: set the denominator equal to zero and solve
then say "all real numbers except those"

Answer 2

shouldn't be too bad for this one since the denominator factors
\[x^2-3x-4=0\]
\[(x-4)(x+1)=0\]
\[x=4, x=-1\] so all numbers except those

Answer 3

Okay:) that seems simple enough.

Answer 4

that also answers the "vertical asymptote" question
vertical asymptotes are \(x=-1\) and \(x=4\)

Answer 5

kill two birds with on stone on that one

Answer 6

Great!

Answer 7

horizontal asymptote is easy as well
the degree of the numerator is 2
the degree of the denominator is 2
since the degrees are the same, the horizontal asymptote is \(y=\text{ratio of leading coefficients}\)

Answer 8

in your example it is \(y=1\)

Answer 9

\(x\) intercepts, set
\[x^2+x-2=0\] and solve
this one factors too
\[(x-1)(x+2)\]

Answer 10

so \(x\) intercepts are \((1,0)\) and \((-2,0)\)

Answer 11

now to graph by hand, make your horizontal asymptotes and your vertical asymptote and then plot some points, not too many

Answer 12

I thought that was the horizontal asymptote

Answer 13

\(y=1\) is the horizontal asymptote
it is a horizontal line