This video tutorial covers the basics of rational functions, including their definition, graphing techniques, and the identification of vertical and horizontal asymptotes, as well as holes. It provides a step-by-step guide to graphing rational functions and explains how to use graphing calculators effectively. The tutorial also includes several example problems to reinforce the concepts discussed.

What is a rational function?

• A function that is always quadratic

• A function that can be written as a ratio of two polynomials

• A function that is always linear

• A function that has no asymptotes

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CCSS.HSF-IF.C.7D

What is an asymptote?

• A line that the graph approaches but never touches

• A point where the graph intersects the y-axis

• A line that the graph crosses

• A point where the graph intersects the x-axis

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CCSS.HSF-IF.C.7D

How is a hole in a rational function graph identified?

• By finding the degree of the numerator

• By finding the zeros of the denominator

• By finding the zeros of the numerator

• By finding common factors that cancel out in the numerator and denominator

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CCSS.HSF-IF.C.7D

What is the first step in graphing a rational function?

• Finding the vertical asymptotes

• Finding the x-intercepts

• Finding the y-intercepts

• Factoring and simplifying the function

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CCSS.HSF-IF.C.7D

How do you find the x-intercepts of a rational function?

• By finding the degree of the denominator

• By finding the degree of the numerator

• By setting the denominator equal to zero and solving

• By setting the numerator equal to zero and solving

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CCSS.HSF-IF.C.7D

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

• There is no horizontal asymptote

• The horizontal asymptote is the x-axis

• The horizontal asymptote is y = 0

• The horizontal asymptote is the leading coefficient of the numerator divided by the leading coefficient of the denominator

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CCSS.HSF-IF.C.7D

What is the domain of a rational function?

• All real numbers except where the denominator is zero

• All real numbers except where the numerator is zero

• All real numbers except where the function has a hole

• All real numbers except where the function is undefined

In the example where the function is simplified to x - 5, what type of function is it?

• Exponential function

• Quadratic function

• Rational function

• Linear function

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What happens when a rational function has two vertical asymptotes?

• The graph will have no asymptotes

• The graph will have two separate hyperbolic curves

• The graph will be a straight line

• The graph will have a single hyperbolic curve

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CCSS.HSF-IF.C.7D

What is the range of a rational function with a horizontal asymptote at y = 2 and a y-intercept at 4.5?

• All y-values less than 2 and greater than 4.5

• All y-values greater than 2 and less than 4.5

• All y-values except y = 4.5

• All y-values except y = 2

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CCSS.HSF-IF.C.7D