Question

i need help finding the x and y intercepts of a rational function PLEASE HELP!!!1

Answer 1

and the rational function is...?

Answer 2

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

Answer 3

i know that when i factor this out it is (x+2)9x-1)/(x+1)(x-4)

Answer 4

i mean (x+2)(x-1)/(x+1)(x-4)

Answer 5

right

Answer 6

so what do you think would be the values of x that would make your denominator equal to 0?

Answer 7

^this is to determine the limits of the x

Answer 8

are they (1,0) (-2,0) and (0, 0.5)

Answer 9

where did 0.5 come from?

Answer 10

wouln't that be they y intercept?

Answer 11

oh yeah sorry...i was imagining x

Answer 12

ok how would i find the domain for this function?

Answer 13

the domain...as i said a while ago...is the limit of x...so find the values of x that would make the denominator = 0

Answer 14

would it be \[(\infty, -1) \cup (-1,4) \cup (4, \infty)\]

Answer 15

yes

Answer 16

except the first should be (\(-\infty\), -1)

Answer 17

yes my mistake
another question is how can i find the horizontal asymptote

Answer 18

horizontal asymptote is the value that makes x equal to infinity

Answer 19

value of y^

Answer 20

ok so does that mean that there is no horizontal aymptote in this function?

Answer 21

do you know how to solve for the range?

Answer 22

you have to solve the range first before judging

Answer 23

the range is all real numbers

Answer 24

so does that mean that the horizontal asymptote is none

Answer 25

anyone?

Answer 26

If you have a rational function where the numerator and denominator have the same degree, which they do here, the asymptote can be found by dividing the coefficients of the highest degree term. So, the numerator has a x^2 with coefficient 1, and the denominator has a x^2 with coefficient 1, so the asymptote is y=1/1=1

Answer 27

does that mean that the horizontal asymptote is 1?

Answer 28

but i thought that the horizontal asymptote was 0

Answer 29

i just need to know what the horizontal asymptote is

Answer 30

>does that mean that the horizontal asymptote is 1?
@redjess13

Yes, the horizontal asymptote is y = 1.