4f Example 1 Part 3 (How to graph the Cotangent Function)

The video tutorial covers the properties and transformations of the cotangent function, including its period, phase shift, and asymptotes. It explains how to graph the cotangent function, highlighting the effects of reflections and shifts. The tutorial also discusses the domain and range of cotangent functions and provides insights into vertical and horizontal transformations. Key concepts such as the relationship between cotangent and other trigonometric functions are explored, with practical examples and sketches to aid understanding.

What is the period of the cotangent function?

• 2π / 2B

• π / 2B

• π / B

• 2π / B

How does the negative sign in the cotangent function affect its graph?

• It reflects the graph about the y-axis

• It changes the period

• It shifts the graph vertically

• It has no effect

Where does the vertical asymptote occur for the cotangent function?

• At 0

• At π/2

• At π

• At 2π

What is the equation for the asymptotes of the cotangent function?

• X = 3π N

• X = π/2 N

• X = 2π N

• X = π N

How does a vertical stretch affect the cotangent graph?

• It reflects the graph

• It shifts the graph horizontally

• It makes the graph narrower

• It makes the graph wider

What is the domain of the cotangent function?

• All real numbers except where X = 2π N

• All real numbers except where X = π N

• All real numbers except where X = π/2 N

• All real numbers except where X = 3π N

What transformation occurs when the cotangent function is shifted π units to the left?

• The graph reflects about the x-axis

• The period changes

• The graph shifts vertically

• The graph shifts horizontally

How does the reflection about the x-axis affect the cotangent graph?

• It inverts the graph

• It shifts the graph

• It changes the period

• It changes the amplitude

What is the range of the cotangent function?

• Negative Infinity to Infinity

• 1 to -1

• 0 to Infinity

• Negative Infinity to 0

Which trigonometric functions have the same asymptote equations as cotangent?

• Sine and Cosine

• Cosecant and Tangent

• Secant and Cosecant

• Tangent and Secant