Tangent Function and Its Properties

The video tutorial explores the behavior of graphs, focusing on how they change and the role of fractions in these changes. It introduces the concept of asymptotes, explaining their significance and how they are drawn. The tutorial also delves into the periodic nature of graphs, particularly the differences between sine, cosine, and tangent functions, highlighting their unique periodicity and behavior.

What happens to the tangent function between two points where it initially increases and then decreases?

• It remains constant.

• It forms a straight line.

• It shows a sudden drop.

• It oscillates.

How does increasing the numerator of a fraction affect its value?

• The fraction decreases.

• The fraction becomes zero.

• The fraction remains the same.

• The fraction increases.

What is the effect of both the numerator increasing and the denominator decreasing on a fraction?

• The fraction decreases.

• The fraction becomes zero.

• The fraction remains the same.

• The fraction increases significantly.

What is the result of dividing a number by zero?

• The result is infinity.

• The result is zero.

• The operation is undefined.

• The result is one.

What is the name of the vertical lines that the tangent graph approaches but never touches?

• Axes

• Intercepts

• Tangents

• Asymptotes

At what angle does the tangent function have an asymptote?

• 360 degrees

• 180 degrees

• 90 degrees

• 45 degrees

How does the tangent function behave as it approaches an asymptote?

• It becomes a straight line.

• It oscillates.

• It approaches infinity.

• It becomes zero.

What is the periodicity of the tangent function?

• 90 degrees

• 180 degrees

• 360 degrees

• 270 degrees

How does the periodicity of the tangent function compare to that of sine and cosine?

• Tangent is not periodic.

• Tangent is periodic every 180 degrees.

• Tangent is periodic every 90 degrees.

• Tangent is periodic every 360 degrees.

What happens to the tangent graph between 0 and 180 degrees?

• It mirrors the graph from 180 to 360 degrees.

• It remains constant.

• It forms a straight line.

• It oscillates.