Question

When asked to sketch the equation y = (x² / (x - a)), can someone explain to me why does the oblique asymptote cuts the y-axis at 'a' ?

Answer 1

Do you know what end behavior is?

Answer 2

Yes, it is a hyperbola. I got the answer but didnt understand why the oblique asymptote cuts the y-axis at 'a'

Answer 3

Oh ok, well when the the degree is bigger in the numerator than in the denominator then we have to go and divide and take the answer as the "slant"or oblique asymptote

Answer 4

So we would have to do \[\Large \frac{x^2}{x-a}\]

Answer 5

As a division problem
Can you divide those out for me and tell me what you get?

Answer 6

yaa, i got the equation for the oblique asymptote y = x+a

Answer 7

vertical asymptote is x=a, stationary points are (0,0) and (2a,4a)

Answer 8

y = x+a

when x=0, y=a

Answer 9

i got the answer.. my question is why does the oblique asymptote, y = x+a, cuts the y-axis at 'a'

Answer 10

its a line with y-intercept at "a"

Answer 11

uhm.. dumbcow how did you get the y-intercept at 'a' ?

Answer 12

OH I GOT IT. OMGGG IM SO DUMB LOOOL

Answer 13

`y = mx + b`

y intercept = `b`

Answer 14

from the equation of the line
--> y = x +a

y-intercept is where x=0

Answer 15

Yeah, you got it, ok? Lol

Answer 16

thanks gais :3 sorry for da trouble >.<

Answer 17

:)

Answer 18

alternatively, since every point on y axis has x value of 0, plugin x = 0 in any equation and solve y to get all the y intercepts

Answer 19

y axis is just an infinite line with all the points whose x values are 0 - so plugging in x = 0 in an equation gives you the points that are common to both the y axis and the curve represented by given equation.

Answer 20

okie thank you kind sir :D