Understanding Vertical Asymptotes in Rational Functions

The video tutorial explains how to find vertical asymptotes in rational functions. It highlights that vertical asymptotes occur when the denominator is zero but the numerator is not. If both are zero, a hole appears in the graph. The tutorial demonstrates factoring the denominator to find values that make it zero, identifying vertical asymptotes and holes. Simplifying the function by canceling common factors helps in determining the vertical asymptotes.

What condition must be met for a vertical asymptote to occur in a rational function?

• The numerator must be zero.

• The denominator must be zero while the numerator is not zero.

• Both the numerator and denominator must be zero.

• The function must be undefined.

What happens when both the numerator and denominator of a rational function are zero?

• The function has no solution.

• A vertical asymptote occurs.

• A hole appears in the graph.

• The function is undefined.

What is the first step in finding vertical asymptotes of a rational function?

• Factor the denominator.

• Factor the numerator.

• Simplify the entire function.

• Set the numerator equal to zero.

In the example provided, what values make the denominator zero?

• x = 3 and x = -2

• x = -3 and x = 2

• x = 1 and x = -1

• x = 0 and x = 1

What is the result when x = 2 is substituted into the example function?

• A vertical asymptote occurs.

• The function is undefined.

• A hole appears in the graph.

• The function equals zero.

What is the vertical asymptote in the example function?

• x = -3

• x = 2

• x = 3

• x = -2

What is the purpose of canceling common factors in a rational function?

• To make the function continuous.

• To eliminate the numerator.

• To simplify the function and identify vertical asymptotes.

• To find the horizontal asymptotes.

After simplification, what determines the vertical asymptote of a rational function?

• The function being undefined.

• Both numerator and denominator being zero.

• The denominator being zero.

• The numerator being zero.

What happens to the values of x that give 0/0 after simplification?

• They are solutions to the function.

• They become vertical asymptotes.

• They are ignored.

• They create holes in the graph.

Why is it important to factor the denominator when finding vertical asymptotes?

• To identify values that make the denominator zero.

• To find the x-intercepts.

• To simplify the numerator.

• To determine the domain of the function.