Tangent Function Transformations and Properties

In this video, Mario from Mario's Math Tutoring explains how to graph tangent functions. He begins by discussing the challenges students face with tangent graphs and reviews the unit circle. The video covers the parent function of tangent graphs, their period, and how to adjust the graph when coefficients are involved. Mario provides examples, including vertical stretching and horizontal shifts, to illustrate these concepts. The video concludes with encouragement to explore further and improve understanding of tangent graphs.

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

• 1

• Undefined

• -1

• 0

What is the period of the parent tangent function?

• π

• 2π

• π/2

• 4π

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

• π

• 2π

• π/2

• 4π

What happens to the x-values when graphing y = tan(1/2x)?

• They are squared

• They are divided by 2

• They are multiplied by 2

• They remain unchanged

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

• Horizontal compression

• Vertical compression

• Vertical stretch

• Horizontal stretch

What is the period of y = 2tan(4x)?

• π/4

• 2π

• π/2

• π

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

• Right π/4

• Down π/4

• Left π/4

• Up π/4

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

• Vertical compression

• Horizontal compression

• Horizontal shift

• Vertical stretch

In y = tan(x - π/4), what happens to the asymptotes?

• Shift down

• Shift left

• Shift up

• Shift right

What is the general effect of adding a constant to x in a tangent function?

• Vertical shift

• Horizontal shift

• Vertical stretch

• Horizontal stretch