Understanding Rational Functions

This video tutorial explains how to find the domain of a rational function, identify vertical and horizontal asymptotes, and graph the function using a graphing calculator. It covers setting the denominator to zero to find excluded values, using these values to determine vertical asymptotes, and plotting the function by selecting appropriate x-values. The tutorial also discusses the behavior of the function as x approaches infinity, leading to a horizontal asymptote.

What is the first step in determining the domain of a rational function?

• Graphing the function

• Using a graphing calculator

• Setting the denominator equal to zero

• Finding the zeros of the numerator

What happens at the values where the denominator of a rational function is zero?

• The function has vertical asymptotes

• The function is defined

• The function has a hole

• The function crosses the x-axis

Why are vertical asymptotes important when sketching a graph?

• They indicate where the graph will cross the x-axis

• They show where the graph will approach but never cross

• They determine the y-intercept

• They are points where the graph is undefined

Which values should be selected when setting up a table of values for graphing?

• Only negative values

• Only positive values

• Values close to the excluded values

• Values far from the excluded values

What feature of the graphing calculator is used to complete the table of values?

• Trace feature

• Table feature

• Graph feature

• Zoom feature

What is the significance of the symmetry observed in the graph of a rational function?

• It helps in predicting y-values

• It indicates the function is linear

• It shows the function is quadratic

• It is irrelevant to graphing

What happens to the value of a rational function as the denominator becomes very large?

• The function value remains constant

• The function value becomes undefined

• The function value approaches zero

• The function value approaches infinity

What is a horizontal asymptote in the context of rational functions?

• A line the graph will never cross

• A line the graph can cross

• A point where the function is undefined

• A point where the function is zero

Can a rational function cross a horizontal asymptote?

• Only if the function is quadratic

• Only if the function is linear

• No, it cannot

• Yes, it can

What are the vertical asymptotes for the given rational function?

• x = 0

• x = 2 and x = -2

• x = 1 and x = -1

• x = 3 and x = -3