Graphing Rational Functions: Domain and Asymptotes

The video tutorial explains how to determine the domain of a rational function by identifying values that make the denominator zero. It covers factoring the function, identifying vertical asymptotes and holes, and using a graphing calculator to complete a table of values. The tutorial also discusses plotting the function and determining horizontal asymptotes, providing a comprehensive guide to analyzing and graphing rational functions.

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

• Plot the function on a graph

• Identify the coefficients of the function

• Set the denominator equal to zero

• Factor the numerator and denominator

Which x-values must be excluded from the domain of a rational function?

• All negative x-values

• Values that result in the numerator being zero

• Values where the function intersects the y-axis

• Values that make the denominator zero

What happens at x = 3 in the given rational function?

• The function crosses the x-axis

• The function has a hole

• There is a vertical asymptote

• The function reaches its maximum value

What is the purpose of placing x = -2 in the middle of the table of values?

• To balance the positive and negative values

• To highlight the y-intercept

• To emphasize the function's minimum value

• To center around the vertical asymptote

Why do we use a graphing calculator when plotting the function?

• To manually draw the graph

• To determine the function's limits

• To find the exact values of x and y

• To save time and improve accuracy

What does a vertical asymptote in a graph represent?

• A value x cannot equal

• A discontinuity in the function

• The slope of the function

• The maximum value of the function

What is indicated by a hole in the graph of a rational function?

• The function's derivative is zero

• A vertical asymptote

• An undefined point in the domain

• A common factor in the numerator and denominator

How is a horizontal asymptote determined?

• By finding the function's maximum value

• By the ratio of the leading coefficients

• By setting the numerator equal to zero

• By the x-values where the function is undefined

What does the function approaching y = 1 signify?

• The function has no horizontal asymptote

• Y = 1 is a horizontal asymptote

• The function has a discontinuity at y = 1

• Y = 1 is where the function has a maximum

Why is the function undefined at x = -2?

• The denominator equals zero at x = -2

• The numerator equals zero at x = -2

• The function intersects the y-axis at x = -2

• The function has a hole at x = -2