Question

Given the following rational function, find the intercepts and asymptotes

Answer 1

\[r(x)=\frac{ 2x^2+7x-15 }{ x^2-8x+15 }\]

Answer 2

@mathmale thank you

Answer 3

I need to find the
xintercept
y intercept
vertical asymptote
horizontal asymptote
and
slant asymptote

Answer 4

I'd strongly suggest that you begin by factoring both numerator and denominator.

Vertical asymptotes: set the 2 factors of the denominator = to zero separately. You'll come up with two equations in x: x= a and x = b. These are your vertical asymptotes.

Would you now please factor the denominator?

Answer 5

(x-3)(x-5)

Answer 6

Great, and now set each one = to 0.
The first one produces the vert. asy. x=3; the other one produces ... ?

Answer 7

3, 5

Answer 8

Not quite; x=3 and x=5 are equations and are the correct descriptors of your vert. asymptotes.

Please write that down: vert. asy. are x=3 and x=5 (equations).

Answer 9

okay so vertical retricemptote: x=3, x=5

Answer 10

asymptote* lol

Answer 11

Right!
Now for the vertical intercept. Simply take the original function and set x = 0. Find y. That's your vert. intercept. Write it as a point: (0, d), where d is the value of your function when x = 0.

Answer 12

So ii dont need to factor numerator?

Answer 13

Lastly, to find the horiz intercepts, please set the numerator (only) in factored form equal to zero (0) and solve for x. You'll get two results: x = c and x = d. Yes, you DO need to factor the numerator. ;(

Answer 14

-15?

Answer 15

Em, I'm not sure what y ou mean by -5. Label that please. for example, "The vertical intercept is (0,-15)." Actually, it's not (0,-15).

If you want the vert. int., set x=0 and find y. What is y when x = 0?

Answer 16

(0,0)

Answer 17

Hint: when x=0, y=(-15) /15 = ?

Answer 18

-1?

Answer 19

so (0,-1)

Answer 20

is that not right?

Answer 21

Wonderful. Write: My y-intercept is (0,-1)."

Lastly, please factor the numerator and set each factor equal to 0. That will give y ou two equations: x=c and x=d. Find c and d.

Excuse my, Em, but i need to get off the Internet. Delighted to be able to work with you again.

Answer 22

I am still a little confuused on how to get my x intercept, horizontal asymptote and slant asympt. If /when u have time please/thanks