Exploring Vertical Asymptotes in Rational Functions

What does it mean when the limit of a function as x approaches a value from the left is negative infinity?

• The function is approaching zero.

• The function is undefined.

• The function is decreasing without bound.

• The function is increasing without bound.

If the limit of a function as x approaches -5 from the right is positive infinity, what is happening to the function?

• The function is undefined.

• The function is decreasing without bound.

• The function is approaching zero.

• The function is increasing without bound.

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

• Factor the denominator.

• Factor the numerator.

• Set the denominator equal to zero.

• Set the numerator equal to zero.

When approaching a vertical asymptote from the left, if the function goes to negative infinity, what does this indicate?

• The function is decreasing without bound.

• The function has a hole.

• The function is undefined.

• The function is increasing without bound.

What happens to the function as x approaches 2 from the right if the limit is positive infinity?

• The function is decreasing without bound.

• The function is approaching zero.

• The function is increasing without bound.

• The function is undefined.

How can you identify vertical asymptotes without a graph?

• By factoring the denominator.

• By factoring the numerator.

• By setting the denominator equal to zero.

• By setting the numerator equal to zero.

What is the impact of multiplicity on vertical asymptotes?

• It has no impact.

• It reinforces the vertical asymptote.

• It cancels out the asymptote.

• It creates a hole in the graph.

In the context of rational functions, what does the domain represent?

• All possible y-values except where the numerator is zero.

• All possible x-values except where the numerator is zero.

• All possible x-values except where the denominator is zero.

• All possible y-values.

What is a horizontal asymptote?

• A line the graph approaches as x goes to infinity or negative infinity.

• A point where the function is undefined.

• A line the graph approaches as y goes to infinity or negative infinity.

• A vertical line the graph never touches.

What does the end behavior of a function describe?

• The behavior of the function as y approaches a specific value.

• The behavior of the function as x approaches infinity or negative infinity.

• The behavior of the function as x approaches a specific value.

• The behavior of the function as y approaches infinity or negative infinity.