Give the equation of a rational function with a horizontal asymptote of 0, exactly one hole, and exactly
one vertical asymptote such that the domain of the function is (−∞, −1) ∪ (−1,4) ∪ (4, ∞).

Discuss: Constructing a Rational Function from its Asymptotes Give an example of a rational function that has a vertical asymptote . Now give an example of one that has vertical asymptote and horizontal asymptote . Now give an example of a rational function with vertical asymptotes and , horizontal asymptote , and intercept 4.

Consider the given function:

a. Find the vertical asymptote(s). If there is more than one vertical asymptote give a list of the -values separated by commas. If there is no vertical asymptote, answer none. 

b. If this function has a horizontal asymptote, give its -value. If there is no horizontal asymptote, answer none. 

c. Find the -intercept(s). If there is more than one -intercept give a list of the -values separated by commas. 

d. Find the -intercept. 

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.