Tangent Function Properties and Periods

Mario from Mario's Math Tutoring explains how to graph tangent functions, focusing on understanding the unit circle, identifying the parent function, and determining the period. He provides examples of graphing tangent functions with different coefficients, demonstrating vertical stretching and horizontal shifting. The video aims to simplify the process and help students overcome common challenges with tangent graphs.

What is the value of the tangent function at -π/2?

• Undefined

• -1

• 1

• 0

What is the period of the parent tangent function?

• 4π

• 2π

• π

• π/2

How does the graph of y = tan(x) behave at x = π/2?

• It crosses the x-axis.

• It reaches a maximum.

• It is undefined.

• It reaches a minimum.

How do you calculate the period of y = tan(1/2x)?

• π divided by 1/2

• π divided by 2

• 2π

• π multiplied by 2

What happens to the tangent graph at π/4?

• It is undefined.

• It reaches a minimum.

• It crosses the x-axis.

• It reaches a maximum.

What is the value of tan(0)?

• 1

• 0

• Undefined

• -1

What is the effect of the coefficient 2 in y = 2tan(4x)?

• It shifts the graph to the right.

• It compresses the graph horizontally.

• It stretches the graph vertically.

• It shifts the graph to the left.

In the function y = 2tan(4x), what is the new period?

• 2π

• π

• π/2

• π/4

How does the graph of y = tan(x - π/4) shift?

• Down by π/4

• Up by π/4

• Right by π/4

• Left by π/4

What is the effect of subtracting π/4 in y = tan(x - π/4)?

• Vertical stretch

• Horizontal compression

• Vertical shift

• Horizontal shift