Question

Explain why a vertical asymptote occurs in a particular location based on the equation of the rational function.

A) Due to the denominator being zero at that point
B) Due to the numerator being zero at that point
C) Due to both numerator and denominator being zero at that point
D) Vertical asymptotes occur randomly and cannot be explained based on equations

Answer 1

A vertical asymptote occurs when the denominator of a rational function is zero at a particular location, resulting in a vertical line that serves as a boundary for the graph.

The Correct Option is; A) Due to the denominator being zero at that point.

Step-by-step explanation:

A vertical asymptote occurs in a particular location based on the equation of a rational function when the denominator of the function is zero at that point (Option A).

A vertical asymptote occurs when the denominator of a rational function is zero at a particular location, resulting in a vertical line that serves as a boundary for the graph.

This happens because division by zero is undefined, and as the denominator approaches zero, the function approaches infinity or negative infinity. This results in a vertical line that serves as a boundary for the graph of the function.