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) = \frac{20 + 5x}{x} $ recall the general form of a rational function: $ f(x) = \frac{(a_m x^m + \dots + a_1 x + a_0)}{(b_n x^n + \dots + b_1 x + b_0)} $ which statement defines the horizontal asymptote? $ \circ $ $ m n $, so there is no horizontal asymptote. done

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) = \frac{20 + 5x}{x} $ recall the general form of a rational function: $ f(x) = \frac{(a_m x^m + \dots + a_1 x + a_0)}{(b_n x^n + \dots + b_1 x + b_0)} $ which statement defines the horizontal asymptote? $ \circ $ $ m < n $, so $ y = 0 $ is the horizontal asymptote. $ \circ $ $ m = n $, so $ y = a_m / b_n $ is the horizontal asymptote. $ \circ $ $ m = n $, so $ y = 0 $ is the horizontal asymptote. $ \circ $ $ m > n $, so there is no horizontal asymptote. done

Accepted Answer

# Explanation:
## Step1: Analyze the degrees of numerator and denominator
For the function $f(x)=\frac{20 + 5x}{x}$, rewrite it as $f(x)=\frac{5x+20}{x}$. 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: Apply the rule for horizontal asymptotes of rational functions
For a rational function $y=\frac{a_mx^m+\cdots+a_0}{b_nx^n+\cdots + b_0}$, when $m = n$, the horizontal asymptote is $y=\frac{a_m}{b_n}$. Here, $a_m = 5$ (coefficient of $x$ in the numerator) and $b_n=1$ (coefficient of $x$ in the denominator).

# Answer:
$m = n$, so $y=a_m/b_n$ is the horizontal asymptote.

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze the degrees of numerator and denominator

Step2: Apply the rule for horizontal asymptotes of rational functions

Answer: