Question

Which is a rational function?
a. y= x-3^x / x^2. b. y= x^2 - x + 4. c. y= x-5/ 2. d. y= 2/x​

Answer 1

ANSWER

d.

$y = \frac{2}{x}$

EXPLANATION

A rational function is of the form:

$r(x) = \frac{p(x)}{q(x)}$

where p(x) and q(x) are polynomial functions and q(x)≠0.

The first option contains the exponential function

${3}^{x}$

This disqualifies it from being a rational function.

The second and third options are polynomial functions.

By definition, all polynomials are rational functions.

The last option is a typical rational function because it has at least an asymptote.

The most correct choice is

$y = \frac{2}{x}$