Question

Identify the horizontal asymptotes, if they exist, for the following function… Option E is cut off, but it says:y = 0

Answer 1

In order to check if there is a horizontal asymptote, we need to analyse the degree of the numerator and denominator.

Since the degree of the numerator (5 from 2x^5) is equal to the degree of the denominator (5 from -7x^5), the horizontal asymptote is given by the division of coefficients of each higher order term, so we have:

`\begin{gathered} 2x^5\to coefficient=2 \\ -7x^5\to coefficient=-7 \\ \\ \text{horizontal asymptote:} \\ y=(2)/(-7)=-(2)/(7) \end{gathered}`

Therefore the correct option is b.