Sketch a graph of a single function that has these properties.
-Find

Question

Quizplus · Accepted Answer

A single function cannot have more than one y-intercept, so options A and D can be eliminated. Option C has exactly one y-intercept, but it also has two horizontal asymptotes, which means it must be a rational function. Option B, on the other hand, has only one horizontal asymptote and can be a sinusoidal function with a vertical shift. Therefore, B is the best choice. The graph should have a horizontal asymptote at y = 7 (option B has this), a vertical asymptote at x = -3 (option B has this), and a local maximum at x = 2 (option B also has this). Option A has a vertical asymptote at x = -2 instead of -3, option C has a vertical asymptote at x = -4 instead of -3, and option D has a local maximum at x = -2 instead of 2.

Sketch a Graph of a Single Function That Has These