Question

Identify whether each formula defines a rational function. If so, identify two polynomials whose ratio comprises it. l(t) = 9t^-3 + 3t^2

Answer 1

we have

$I(t)=9t^{-3}+3t^2$

Applying property of exponents

$I(t)=\frac{9}{t^3}+3t^2$

Adds the terms

$\begin{gathered} I(t)=\frac{9+t^3\cdot3t^2}{t^3} \\ \\ I(t)=\frac{3t^5+9}{t^3} \end{gathered}$

we have a rational function

the two polynomials are

numerator ------> 3t^5+9 (binomial of degree 5)

denominator ----> t^3 (monomial of degree 3)