Graphing Rational Functions in Pre Calculus

The video tutorial, led by Mr. Sullivan, pays tribute to Mr. Bean while teaching about graphing rational functions. It covers the definition and properties of rational functions, including domains, intercepts, and asymptotes. The tutorial explains how to find horizontal and slant asymptotes using polynomial division and demonstrates graphing techniques for rational functions, emphasizing the importance of identifying holes and asymptotes.

What is a rational function?

• A polynomial divided by a constant

• A polynomial divided by another polynomial

• A constant divided by a polynomial

• A polynomial multiplied by another polynomial

What must be true for the denominator of a rational function?

• It must be a constant

• It cannot be zero

• It can be zero

• It must be a polynomial of degree one

What happens when a factor in the denominator cancels with a factor in the numerator?

• It creates a vertical asymptote

• It creates a slant asymptote

• It creates a hole

• It creates a horizontal asymptote

How do you find the y-intercept of a rational function?

• Set the denominator to zero

• Set both x and y to zero

• Set x to zero and solve for y

• Set y to zero and solve for x

What is the x-intercept of a rational function?

• Where the graph crosses the y-axis

• Where the numerator is zero

• Where the graph crosses the x-axis

• Where the denominator is zero

What determines the horizontal asymptote of a rational function?

• The coefficients of the numerator

• The degree of the numerator

• The degree of the denominator

• The degrees of both the numerator and the denominator

When does a rational function have a slant asymptote?

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

• When the degree of the denominator is greater than the degree of the numerator by one

• When the degree of the numerator is equal to the degree of the denominator

• When the degree of the numerator is greater than the degree of the denominator by one

What is the first step in graphing a rational function?

• Finding the y-intercepts

• Finding the x-intercepts

• Identifying holes and asymptotes

• Simplifying the function

What tool can be used to graph rational functions easily?

• A ruler and pencil

• A spreadsheet software

• Desmos.com

• A scientific calculator

What must be marked on the graph if there is a hole at a certain x-value?

• A vertical line

• A filled circle

• A horizontal line

• An open circle