Question

use the graphs of the rational functions in a to d on the right to answer the question. give all possible answers, as there may be more than one correct choice. which graphs have the x - axis as a horizontal asymptote? select all the graphs that apply. graph a graph b graph c graph d

Explanation:

Step1: Identify x-axis asymptote rule

A rational function has the x-axis ($y=0$) as a horizontal asymptote if the degree of the numerator is less than the degree of the denominator, and the graph approaches $y=0$ as $x\to\pm\infty$.

Step2: Analyze each graph

• Graph A: Approaches $y=0$ (x-axis) as $x\to\pm\infty$, so x-axis is horizontal asymptote.
• Graph B: Approaches a non-zero horizontal line (not x-axis) as $x\to\pm\infty$, so x-axis is not its horizontal asymptote.
• Graph C: Approaches $y=0$ (x-axis) as $x\to\pm\infty$, so x-axis is horizontal asymptote.
• Graph D: Approaches $y=0$ (x-axis) as $x\to\pm\infty$, so x-axis is horizontal asymptote.

Answer:

A. Graph A, C. Graph C, D. Graph D