Analyzing Asymptotes in Rational Functions

What is a rational function?

• A function that can be written as a polynomial added to another polynomial.

• A function that can be written as a polynomial subtracted from another polynomial.

• A function that can be written as a polynomial multiplied by another polynomial.

• A function that can be written as a polynomial divided by another polynomial.

What is a horizontal asymptote?

• A point where the graph intersects the y-axis.

• A point where the graph intersects the x-axis.

• A line that the graph approaches but never touches, running left to right.

• A line that the graph approaches but never touches, running up and down.

How are vertical asymptotes represented?

• As equations in the form x = a number.

• As curves on the graph.

• As equations in the form y = a number.

• As points on the graph.

How do you find the domain of a rational function?

• By setting the denominator equal to zero.

• By finding the intersection points with the x-axis.

• By finding the intersection points with the y-axis.

• By setting the numerator equal to zero.

What does it mean if the degree of the numerator is equal to the degree of the denominator?

• The horizontal asymptote is y = 0.

• There is no horizontal asymptote.

• The vertical asymptote is x = 0.

• The horizontal asymptote is the ratio of the leading coefficients.

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

• y = 1

• y = the ratio of the leading coefficients

• y = 0

• There is no horizontal asymptote

What is the horizontal asymptote if the degree of the numerator is greater than the degree of the denominator?

• y = the ratio of the leading coefficients

• There is no horizontal asymptote

• y = 1

• y = 0

How do you find vertical asymptotes?

• By finding the intersection points with the y-axis.

• By finding the intersection points with the x-axis.

• By setting the denominator equal to zero and solving.

• By setting the numerator equal to zero and solving.

What happens if you get imaginary solutions when solving for vertical asymptotes?

• There are no vertical asymptotes.

• The vertical asymptotes are imaginary.

• The vertical asymptotes are at y = 0.

• The vertical asymptotes are at x = 0.

What is the horizontal asymptote for the function f(x) = (3x^3 + 2x^2) / (x^2 + 1)?

• There is no horizontal asymptote

• y = 3

• y = 2

• y = 0