Graph Behavior and Asymptotes

This video tutorial explores the graph of a rational function, focusing on end behaviors as X approaches negative and positive infinity, and the behavior near vertical asymptotes. It explains the concept of asymptotes, both vertical and horizontal, and how they affect the graph. The video also covers intervals of increase and decrease, and provides a detailed analysis of the domain and range of the function. Key concepts such as end behavior, asymptotes, and graph analysis are highlighted throughout the tutorial.

What is the primary focus of this video tutorial?

• Analyzing the graph of a polynomial function

• Understanding the graph of a rational function

• Exploring the graph of a trigonometric function

• Studying the graph of an exponential function

As X approaches negative infinity, what does the graph approach?

• A diagonal line

• A point at the origin

• A horizontal line at y = 3

• A vertical line

What happens to the graph as X approaches 1 from the left?

• It approaches positive infinity

• It approaches negative infinity

• It becomes constant

• It crosses the vertical asymptote

As X approaches 1 from the right, what is the behavior of the graph?

• It crosses the horizontal asymptote

• It becomes constant

• It approaches negative infinity

• It approaches positive infinity

What is the end behavior of the graph as X approaches positive infinity?

• It crosses the x-axis

• It becomes a parabola

• It approaches a horizontal line at y = 3

• It approaches a vertical line

What is a vertical asymptote?

• A line that the graph approaches but never crosses

• A line that the graph intersects at one point

• A line that the graph becomes parallel to

• A line that the graph crosses

What is the equation of the horizontal asymptote in this graph?

• y = 0

• y = 1

• y = -1

• y = 3

How does the graph behave in terms of increasing and decreasing intervals?

• It has both increasing and decreasing intervals

• It decreases over the entire domain

• It remains constant

• It increases over the entire domain

What is the domain of the rational function?

• All negative numbers

• All positive numbers

• All real numbers

• All real numbers except x = 1

What is the range of the rational function?

• All negative numbers

• All positive numbers

• All real numbers except y = 3

• All real numbers