# Math Help - Graph help please.

Identify the rational function whose graph is shown in the figure.

Choices are

f(x) = (3x+5)/(x+1)

f(x) = (x+5)/(x+3)

f(x) = (3x-5)/(x-1)

f(x) = (x+5)/(x+1)

2. Originally Posted by wvmcanelly@cableone.net
Identify the rational function whose graph is shown in the figure.

Choices are

f(x) = (3x+5)/(x+1)

f(x) = (x+5)/(x+3)

f(x) = (3x-5)/(x-1)

f(x) = (x+5)/(x+1)

the graph is $f(x) = \frac {3x + 5}{x + 1}$

vertical asymptotes occur when the function is undefined. we see one occurs when x = -1, so we want one of the graphs where the denominator is zero when x = -1. so the first and the last graphs are the possible choices. how do we know which to choose?

from the horizontal asymptote of course. since the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is given by the ratio of the leading coefficients, which for the first is 3/1 = 3 as is in the graph

3. If you are so inclined, see http://www.mathhelpforum.com/math-he...-help-plz.html for more information on vertical and horizontal asymptotes