Question

Is f(t) = 0 a rational function?

Answer 1

Recall that a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.

Let P(t)=0 (the polynomial zero) and Q(t)=1, now, notice that:

`f(t)=0=(0)/(1)=(P(t))/(Q(t))\text{.}`

Since both, P(t) and Q(t) are polynomials, we get that f(t) is a rational function.

Answer: f(t)=0 is a rational function.