Question

shilpas gym membership includes a one-time fee of $20. she then pays a discounted fee of $5 for each visit. the function that shows her average cost after x visits is: f(x) = (20 + 5x)/x recall the general form of a rational function: f(x) = (a_m x^m + + a_1 x + a_0)/(b_n x^n + + b_1 x + b_0) which statement defines the horizontal asymptote? m < n, so y = 0 is the horizontal asymptote. m = n, so y = a_m / b_n is the horizontal asymptote. m = n, so y = 0 is the horizontal asymptote. m > n, so there is no horizontal asymptote. complete the horizontal asymptote is y = 0 5 20 25 done

Explanation:

Step1: Analyze the degrees of numerator and denominator

For the function \( f(x)=\frac{20 + 5x}{x}=\frac{5x+20}{x}\), the degree \(m\) of the numerator \(5x + 20\) (highest - power of \(x\)) is \(m = 1\), and the degree \(n\) of the denominator \(x\) is \(n=1\).

Step2: Use the rule for horizontal asymptotes of rational functions

When \(m = n\) (where \(m\) is the degree of the numerator and \(n\) is the degree of the denominator) for a rational function \(y=\frac{a_mx^m+\cdots+a_0}{b_nx^n+\cdots + b_0}\), the horizontal asymptote is \(y=\frac{a_m}{b_n}\). Here, \(a_m = 5\) (the coefficient of \(x\) in the numerator) and \(b_n=1\) (the coefficient of \(x\) in the denominator).

Answer:

The horizontal asymptote is \(y = 5\)