Question

Shilpa's 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.

Which statement defines the horizontal asymptote?

Answer 1

The horizontal asymptote for the function representing Shilpa's average gym cost after x visits is y = $5, since the initial fee becomes negligible as the number of visits grows infinitely large.

Step-by-step explanation:

The question involves finding the horizontal asymptote of the function representing Shilpa's average cost after x visits to the gym. The formula for this function is given by Average Cost = (Initial fee + (Cost per visit × Number of visits)) / Number of visits. This translates to:

Average Cost = (20 + 5x) / x

As x (the number of visits) approaches infinity, the initial fee of $20 becomes negligible, and the function approaches the cost per visit, which is $5. Therefore, the horizontal asymptote of this function is at y = $5, because as the number of gym visits increases, the average cost per visit approaches $5.

Answer 2

m = n, so y = am / bn is the horizontal asymptote is the answer