Graphing Tangent and Cotangent Functions

The video tutorial explains how to graph tangent and cotangent functions with vertical shifts. It covers identifying key parameters like period, x-scale, and starting points. The tutorial demonstrates graphing the tangent function with a vertical stretch and shift, followed by graphing the cotangent function with a phase shift and vertical transformation. The instructor emphasizes understanding transformations and scaling, providing clear examples and explanations.

What is the role of the parameter 'k' in graphing tangent and cotangent functions?

• It determines the amplitude.

• It indicates a vertical shift.

• It changes the phase.

• It affects the period.

How is the period of a tangent function calculated?

• b times π

• π divided by b

• 2π divided by b

• b divided by π

What is the x-scale for a tangent function if the period is 1?

• 1/5

• 1/2

• 1/3

• 1/4

When graphing a tangent function, what does a vertical stretch involve?

• Decreasing the period

• Changing the starting point

• Increasing the period

• Changing the range of y-values

In the context of graphing, what does a negative starting point indicate?

• A vertical compression

• A shift to the right

• A shift to the left

• A vertical stretch

How is the period of a cotangent function determined when b is 1/2?

• π/2

• 2π

• π

• 4π

What is the x-scale for a cotangent function with a period of 2π?

• π/2

• π

• 2π

• π/4

What does a phase shift in a cotangent function graph involve?

• Shifting the graph horizontally

• Shifting the graph vertically

• Changing the amplitude

• Changing the period

What happens to the graph of a cotangent function when it is shifted up by one unit?

• The period decreases by one unit.

• The period increases by one unit.

• The intercepts move down by one unit.

• The intercepts move up by one unit.

Which transformation does not occur in the cotangent function example discussed?

• Phase shift

• Vertical stretch

• Vertical shift

• Horizontal shift