Master graphing tangent and cotangent with a change in period

The video tutorial explains how to graph tangent and cotangent functions, focusing on changes in period and the effects of parameter 'A' on graph shape. It covers the absence of amplitude in these graphs, the calculation of periods, and the identification of critical points. The tutorial provides detailed steps for graphing both functions, illustrating the impact of vertical stretching and compression.

What is the effect of the parameter 'a' on the tangent and cotangent graphs?

• It shifts the graph horizontally.

• It determines the amplitude.

• It changes the period.

• It affects the vertical stretch or compression.

How does the period of tangent and cotangent functions compare to sine and cosine?

• It is the same as sine and cosine.

• It is twice as long as sine and cosine.

• It is half as long as sine and cosine.

• It is unrelated to sine and cosine.

What is the period of the function y = 3 * tan(x/4)?

• π/4

• 4π

• π

• 2π

In the tangent function graph, what is the significance of the asymptotes?

• They indicate the maximum points.

• They show where the graph crosses the x-axis.

• They are the points of inflection.

• They represent the points where the graph is undefined.

What happens to the tangent graph when the absolute value of 'a' is greater than one?

• The graph is horizontally stretched.

• The graph is vertically compressed.

• The graph is shifted upwards.

• The graph is vertically stretched.

What is the period of the function y = 1/2 * cot(2πx)?

• π

• 2π

• 1

• 1/2

How do you determine the x-scale for the cotangent function y = 1/2 * cot(2πx)?

• Divide the period by 2.

• Multiply the period by 4.

• Divide the period by 4.

• Multiply the period by 2.

What is the effect on the cotangent graph when the absolute value of 'a' is less than one?

• The graph is vertically compressed.

• The graph is horizontally stretched.

• The graph is vertically stretched.

• The graph is shifted downwards.

In the cotangent function graph, what does the x-intercept represent?

• The minimum point of the graph.

• The maximum point of the graph.

• The point where the graph is undefined.

• The point where the graph crosses the x-axis.

What is the reciprocal function of cotangent?

• Secant

• Cosine

• Sine

• Tangent