Module 11: Rational Functions

What is a rational function?

• A rational function is the product of two polynomials.

• A rational function is a single polynomial.

• A rational function is a constant value.

• A rational function is the ratio of two polynomials.

Which of the following is a rational function: 2/x or 3x?

• 5+x

• x^2

• 4/x

• 2/x

If y varies inversely with x, what is the relationship between y and x?

• y = k/x^2, where k is a constant.

• y = k*x, where k is a constant.

• y = k + x, where k is a constant.

• y = k/x, where k is a constant.

True or False: A rational function can have a variable in the denominator.

• A rational function must have a constant denominator

• A rational function cannot have any variables

• True

• False

Graph the function y = 1/x. What does the graph look like?

• The graph of y = 1/x consists of two hyperbolic branches, one in the first quadrant and one in the third quadrant, with vertical and horizontal asymptotes at the axes.

• The graph of y = 1/x has a single branch in the second quadrant only.

• The graph of y = 1/x is a straight line through the origin.

• The graph of y = 1/x is a circle centered at the origin.

If y = k/x, what happens to y as x increases?

• y increases without bound as x increases.

• y decreases towards zero as x increases.

• y remains constant regardless of x.

• y oscillates between positive and negative values as x changes.

Identify the rational function from the following: y = (x+1)/(x-1) or y = x^2 + 1?

• y = (x+1)/(x-1)

• y = x + 1

• y = x^2 - 1

• y = 1/(x^2 + 1)

What is the inverse variation of y = 5/x?

• xy = 5

• y = 5/x^2

• xy = 10

• y = 5x

How do you find the asymptote of the graph of a rational function?

• Horizontal asymptotes are always at y=0 regardless of the degrees.

• Asymptotes are found by calculating the derivative of the function.

• Vertical asymptotes occur where the numerator is zero.

• Vertical asymptotes occur where the denominator is zero; horizontal asymptotes depend on the degrees of the numerator and denominator.

True or False: The graph of y = 1/(x-2) has a vertical asymptote at x = 2.

• False

• The graph does not have a vertical asymptote

• True

• The vertical asymptote is at x = 0