What is an Asymptote Anyway?

Algebra Level 1

How many vertical asymptotes are there on the following rational function?

f ( x ) = x 356 123 x 22 43 x 2 + 10123 x f(x) = \frac{x^{356} - 123x^{22} - 43x^{2}+10123}{x}


The answer is 1.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

We note that any point on a rational function that results in an answer of the form f ( x ) = k 0 , k 0 f(x) = \frac{k}{0}, k \neq 0 is a vertical asymptote. We can set the denominator to zero to find all possible asymptotes. Since the denominator is just x x , we have x = 0 x=0 as the only possible asymptote. We can verify that the answer for f ( 0 ) f(0) is in the form 10123 0 \frac{10123}{0} . By our definition above, this is a vertical asymptote. Thus, the answer is 1 1

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...