vertical asymptotes

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April 29th 2010, 07:02 PM
georget

x-y intercept / horizontal / vertical asymptotes

Okay i'm having trouble figuring out how to do this worksheet. Here are the questions with what i need to get.

For each of these four questions I need to find the x and y intercepts (if any) and the vertical / horizontal asymptotes. I completely forget this section.

1. (x+3) / (1-x^2)

the other three will be added shortly.
April 29th 2010, 07:11 PM
Gusbob

Quote:

Originally Posted by georget

Okay i'm having trouble figuring out how to do this worksheet. Here are the questions with what i need to get.

For each of these four questions I need to find the x and y intercepts (if any) and the vertical / horizontal asymptotes. I completely forget this section.

1. (x+3) / (1-x^2)

the other three will be added shortly.

You have $y = \frac{x+3}{1-x^2}$

x intercepts is point (x,0) where x is the value you get when solving the equation when y = 0.

y intercepts is the point (0, y) where y is the value you get when solving the equation when x=0

Vertical asymptotes is any x that is not in the domain, i.e. when a certain value of x does not have a y value. Hint: denominator cannot be 0. Formally vertical asymptote x = a if $\lim_{x\rightarrow a^+} = \pm \infty$ or $\lim_{x\rightarrow a^-} = \pm \infty$

Horiztonal asymptotes you can find (if any) using
$\lim_{x \rightarrow \pm \infty} f(x)$ . If limit exists, it is the horizontal asymptote.

Please attempt to do this yourself on this question and the other three first.
April 29th 2010, 07:25 PM
georget

Okay i got that one but the other ones i'm having trouble with. Mainly because they are larger numbers and a bit more complex. I have the vertical asymptotes for all of them. Here are the other four

f(x) = (2-x)/(1-x^2)

f(x) = (8x^7 - 32x^5) / (1-x^2)

f(x) = (7x^2 + 63) / (100 + x^2)

f(x) = (3x^2 -75) / (x^2 + 13x)
April 29th 2010, 07:59 PM
pickslides

Quote:

Originally Posted by georget

I have the vertical asymptotes for all of them.

Good, what was the vertical asypmtote for this one?

Quote:

Originally Posted by georget

f(x) = (7x^2 + 63) / (100 + x^2)

??

Quote:

Originally Posted by georget

f(x) = (8x^7 - 32x^5) / (1-x^2)

f(x) = (7x^2 + 63) / (100 + x^2)

f(x) = (3x^2 -75) / (x^2 + 13x)

For these 3 you should divide them out, as the order of the numerator is equal or greater than that of the denominator.
April 29th 2010, 08:03 PM
georget

that one has no vertical asymptote. if i did it correctly and the horizontal is y=7