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)=(9)/(t^3)+3t^2`

Adds the terms

`\begin{gathered} I(t)=(9+t^3\cdot3t^2)/(t^3) \\ \\ I(t)=(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)