Question

find the horizontal asymptote of the following function. give your answer in the form ( y = b ), or enter ( varnothing ) if there is none.

( f ( x ) = \frac { 6 x ^ { 5 } - 4 x ^ { 2 } + 5 } { 6 x ^ { 2 } + 5 x - 4 } )

Explanation:

Step1: Determine the degrees of numerator and denominator

The degree of the numerator \(n = 5\) (from \(6x^{5}\)) and the degree of the denominator \(m=2\) (from \(6x^{2}\)).

Step2: Apply the rule for horizontal asymptotes

When \(n>m\) (here \(5 > 2\)), there is no horizontal asymptote.

Answer:

\(\varnothing\)