Asymptotic Behavior of Functions

The video tutorial explains the end behavior of a rational function's graph as it approaches both horizontal and vertical asymptotes. It describes how the graph approaches a horizontal asymptote at y = 1 as X goes to positive and negative infinity. Additionally, it covers the behavior of the graph near a vertical asymptote at x = 2, detailing how the graph approaches infinity on the positive side and negative infinity on the negative side.

What is the end behavior of a rational function?

• The behavior of the graph as it approaches zero.

• The behavior of the graph as it crosses the y-axis.

• The behavior of the graph as it approaches the x-axis.

• The behavior of the graph as it approaches infinity or negative infinity.

What is a horizontal asymptote?

• A line that the graph approaches as y goes to infinity.

• A line that the graph approaches as x goes to infinity or negative infinity.

• A line that the graph crosses at x = 0.

• A line that the graph never touches.

What is the horizontal asymptote of the given function?

• y = -1

• y = 0

• y = 2

• y = 1

What does the graph of a rational function do as it approaches a horizontal asymptote?

• It oscillates around the asymptote.

• It approaches but never touches the asymptote.

• It crosses the asymptote.

• It moves away from the asymptote.

What does it mean for a graph to have a horizontal asymptote at y = 1?

• The graph will oscillate around y = 1.

• The graph will cross y = 1 at some point.

• The graph will approach y = 1 as x goes to infinity or negative infinity.

• The graph will never reach y = 1.

What is a vertical asymptote?

• A line that the graph crosses at y = 0.

• A line that the graph approaches as y goes to infinity.

• A line that the graph approaches but never crosses.

• A line that the graph approaches as x goes to infinity.

What is the vertical asymptote of the given function?

• x = 2

• x = 1

• x = 0

• x = -2

What is the significance of a vertical asymptote in a rational function?

• It indicates where the graph crosses the x-axis.

• It indicates where the graph crosses the y-axis.

• It indicates a value of x that the function cannot take.

• It indicates a value of y that the function cannot take.

As x approaches positive infinity, what does the graph approach?

• y = -1

• y = 1

• y = 2

• y = 0

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

• y = 1

• y = 2

• y = 0

• y = -1