Final Answer:
The example of a rational function is a) (f(x) = 2x + 1/x² - 4).
Step-by-step explanation:
A rational function is a function that can be expressed as a quotient of two polynomials.
a) (f(x) = 2x + 1/x² - 4) fits this definition:
It has two terms: 2x and 1/x².
Both terms are polynomials (x² is a polynomial of degree 2, and 2x is a polynomial of degree 1).
The function is the quotient of these two polynomials divided by 1 (implicit denominator).
b) (g(x) = √x + 3) has a non-polynomial term (√x) and therefore is not a rational function.
c) (h(x) = 1/sin(x)) has sin(x) in the denominator, making it not a polynomial and hence not a rational function.
d) (k(x) = eˣ + 2) has exponential term (eˣ) which is not a polynomial, thus not a rational function.
Therefore, only option a) satisfies the definition of a rational function.