Graphing Rational Functions: Asymptotes and Discontinuities

The video tutorial covers the process of graphing rational functions, focusing on identifying key elements such as horizontal and vertical asymptotes, holes, and intercepts. The instructor explains how to determine these elements by analyzing the degrees of the numerator and denominator, factoring, and solving equations. The tutorial also includes a demonstration of graphing a rational function and discusses domain restrictions. Viewers are encouraged to practice with a problem provided at the end.

What are the five key attributes needed to graph rational functions?

• Horizontal asymptote, holes, vertical asymptotes, x and y intercepts

• Horizontal asymptote, holes, vertical asymptotes, x intercepts, and slope

• Vertical asymptote, holes, x and y intercepts, and slope

• Horizontal asymptote, holes, vertical asymptotes, y intercepts, and slope

Tags

CCSS.HSF-IF.C.7D

If the degree of the numerator is greater than the degree of the denominator, what is the horizontal asymptote?

• y = the leading coefficient of the numerator divided by the leading coefficient of the denominator

• y = 0

• There is no horizontal asymptote

• y = 1

Tags

CCSS.HSF-IF.C.7D

How do you find the horizontal asymptote when the degrees of the numerator and denominator are equal?

• There is no horizontal asymptote in this case

• Subtract the degree of the denominator from the degree of the numerator

• Set the numerator equal to zero

• Divide the leading coefficient of the numerator by the leading coefficient of the denominator

Tags

CCSS.HSF-IF.C.7D

What is another term for holes in a graph?

• Vertical asymptotes

• Horizontal asymptotes

• Intercepts

• Removable discontinuities

Tags

CCSS.HSF-IF.C.7D

How do you determine the x-coordinate of a hole?

• Set the denominator equal to zero after canceling out common factors

• Find the leading coefficient of the denominator

• Find the leading coefficient of the numerator

• Set the numerator equal to zero

Tags

CCSS.HSF-IF.C.7D

What is the y-coordinate of a hole if the x-coordinate is 5?

• 3

• 5

• 7

• 18/7

Tags

CCSS.HSF-IF.C.7D

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

• Subtract the degrees of the numerator and denominator

• Set the numerator equal to zero

• Set the denominator equal to zero in the simplified function

• Divide the leading coefficients

Tags

CCSS.HSF-IF.C.7D

What is the x-intercept of a rational function?

• The point where the denominator equals zero

• The point where the graph crosses the y-axis

• The point where the graph crosses the x-axis

• The point where the numerator equals zero

Tags

CCSS.HSF-IF.C.7D

What is the y-intercept of a rational function?

• The point where the numerator equals zero

• The point where the denominator equals zero

• The point where the graph crosses the y-axis

• The point where the graph crosses the x-axis

Tags

CCSS.HSF-IF.C.7D

What are domain restrictions in the context of rational functions?

• Values of y that make the denominator zero

• Values of x that make the numerator zero

• Values of x that make the denominator zero

• Values of y that make the numerator zero