1. identify whether the functions shown are rational:
a. f(x) = x / x^2 + 1
b. f(x) = √x / x^2 + 1
c. f(x) = x / x^0.4 + 1
d. f(x) = (x / x^2 + 1)^2
e. f(x) = √2x / ex^2 + √3

a) Rational function

b) Not a rational function

c) Not a rational function

d) Rational function

e) Not a rational function

Step-by-step explanation:

A rational function is of the form;

where and are polynomial functions.

For option a) , we have both the numerator and the denominator are polynomial functions, hence is a rational function.

For option b) , is not a polynomial function hence is not a rational function.

For option c) we have , is not a polynomial function hence is not a rational function.

For option d) both and are polynomials hence   is a rational function.

For option e) both the numerator and the denominator are not polynomials hence    is not a rational function.

b

step-by-step explanation: