Question

find the horizontal asymptote, if any, of the graph of the rational function
$f(x)=\frac{-2x + 3}{7x + 5}$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the horizontal asymptote is
(type an equation. simplify your answer use integers or fractions for any numbers in the equation)
b. there is no horizontal asymptote.

Explanation:

Step1: Recall horizontal asymptote rule

For a rational function \( f(x)=\frac{ax + b}{cx + d} \) (degree of numerator = degree of denominator), the horizontal asymptote is \( y=\frac{a}{c} \).
Here, \( f(x)=\frac{-2x + 3}{7x + 5} \), \( a=-2 \), \( c = 7 \).

Step2: Calculate the horizontal asymptote

Using the rule, \( y=\frac{-2}{7} \).

Answer:

A. The horizontal asymptote is \( y = -\frac{2}{7} \)