Graphing Rational Functions with Removable Discontinuities

The video tutorial covers the process of factoring and simplifying rational expressions, focusing on identifying and handling removable discontinuities. It explains how to graph rational functions, including finding horizontal and vertical asymptotes. The tutorial also demonstrates how to determine x and y intercepts and use sign analysis to understand graph behavior near asymptotes.

What is the first step in simplifying a rational function?

• Factoring the numerator and denominator

• Multiplying the numerator and denominator

• Subtracting the numerator from the denominator

• Adding the numerator and denominator

What happens when a factor cancels out in both the numerator and denominator?

• A vertical asymptote is created

• A horizontal asymptote is created

• The function becomes undefined

• A removable discontinuity is created

How do you find the location of a hole in the graph?

• Set the numerator to zero

• Set the denominator to zero

• Find the x-intercept

• Substitute the value that makes the factor zero into the simplified function

What is the horizontal asymptote of the function y = (x^2 + 2x - 3) / (x^2 - x - 2)?

• y = 1

• y = 0

• y = x

• y = -1

What is the vertical asymptote of the function y = (x^2 + 2x - 3) / (x^2 - x - 2)?

• x = -1

• x = 1

• x = 2

• x = -2

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

• Set y to 0

• Set x to 0

• Set y to 1

• Set x to 1

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

• Set y to 1

• Set x to 1

• Set the denominator to zero

• Set the numerator to zero

What does a positive result in sign analysis indicate about the graph's behavior near a vertical asymptote?

• The graph approaches negative infinity

• The graph remains constant

• The graph approaches positive infinity

• The graph crosses the x-axis

What does a negative result in sign analysis indicate about the graph's behavior near a vertical asymptote?

• The graph remains constant

• The graph approaches negative infinity

• The graph approaches positive infinity

• The graph crosses the y-axis

What is the purpose of sign analysis in graphing rational functions?

• To determine the behavior of the graph near vertical asymptotes

• To determine the horizontal asymptotes

• To find the x-intercepts

• To find the y-intercepts