Understanding Rational Functions

What are the two types of discontinuities discussed in the introduction to rational functions?

• Horizontal asymptotes and slant asymptotes

• Vertical asymptotes and horizontal asymptotes

• Vertical asymptotes and holes

• Holes and slant asymptotes

How do horizontal asymptotes differ from vertical asymptotes?

• Functions can pass through horizontal asymptotes

• Horizontal asymptotes are always at y=0

• Vertical asymptotes can be crossed by functions

• Horizontal asymptotes are boundaries that cannot be crossed

What is the horizontal asymptote when the degree of the numerator is less than the degree of the denominator?

• No horizontal asymptote

• y = 1

• y = a/b

• y = 0

If the degrees of the numerator and denominator are equal, what determines the horizontal asymptote?

• The constant term

• The sum of the coefficients

• The ratio of the leading coefficients

• The difference in degrees

What happens if the degree of the numerator is greater than the degree of the denominator?

• The function has a vertical asymptote

• The function is undefined

• There is no horizontal asymptote

• There is a horizontal asymptote at y = 0

What is a slant asymptote?

• A horizontal line that the graph approaches

• A vertical line that the graph approaches

• A diagonal line that the graph approaches

• A point where the graph is undefined

When does a slant asymptote occur?

• When the degree of the numerator exceeds the denominator by one

• When the degrees of the numerator and denominator are equal

• When the degree of the numerator is less than the denominator

• When the function has no vertical asymptotes

In the example analysis, what is the horizontal asymptote if the degrees of the numerator and denominator match?

• y = 1

• y = 3

• y = 0

• y = 2

What type of discontinuity is present at x = 3 in the example analysis?

• Slant asymptote

• Vertical asymptote

• Horizontal asymptote

• Hole

How is the y-intercept found in the example analysis?

• By setting y to zero

• By finding the horizontal asymptote

• By setting x to zero

• By finding the slant asymptote