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Slant Asymptotes: Find the slant asymptote and the vertical asymptotes, and sketch a graph of the function.

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Jamar Ferry
Jamar FerryLv2
28 May 2020

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Consider the following rational functions:

 

 

 

 

 

 

(a) Which of these rational functions has a horizontal asymptote?

(b) Which of these functions has a slant asymptote?

(c) Which of these functions has no vertical asymptote?

(d) Which of these functions has a hole?

(e) What are the asymptotes of the function ?

(f) Graph , showing clearly any asymptotes and and  intercepts the function may have.

(g) Use long division to find a polynomial that has the same end behavior as . Graph both and on the same screen to verify that they have the same end behavior.

 

Consider the following rational functions:

  

(a) Which of these rational functions has a horizontal asymptote?

(b) Which of these functions has a slant asymptote?

(c) Which of these functions has no vertical asymptote?

(d) Which of these functions has a "hole"?

(e) What are the asymptotes of the function r(x)?

(f) Graph the function y = u(x), showing clearly all the asymptotes, x-intercepts, and y-intercepts that the function may have.

(g) Use long division to find a polynomial P that has the same end behavior as t. Graph both P and t to verify that they have the same end behavior. 

Consider the following rational functions:

 

(a) Which of these rational functions has a horizontal asymptote?

(b) Which of these functions has a slant asymptote?

(c) Which of these functions has no vertical asymptote?

(d) Which of these functions has a "hole"?

(e) What are the asymptotes of the function r(x)?

(f) Graph the function y = u(x), showing clearly all the asymptotes, x-intercepts, and y-intercepts that the function may have.

(g) Use long division to find a polynomial P that has the same end behavior as t. Graph both P and t to verify that they have the same end behavior. 

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