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:
[tex]\begin{gathered} 2x^5\to coefficient=2 \\ -7x^5\to coefficient=-7 \\ \\ \text{horizontal asymptote:} \\ y=\frac{2}{-7}=-\frac{2}{7} \end{gathered}[/tex]
Therefore the correct option is b.
