Tangent Function and Its Properties

In this video, Mario from Mario's Math Tutoring explains how to graph the tangent function. He begins by discussing the challenges students face with tangent graphs and reviews the unit circle. The video covers the parent function, period, and how to graph tangent functions with different coefficients, including examples like y = 2 * tan(4x) and y = tan(x - π/4). Mario provides tips on handling vertical stretches and horizontal shifts, ensuring students understand the graphing process. The video concludes with encouragement to explore more math tutorials.

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

• π/2

• 2π

• π

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

• π

• 2π

• π/2

• 4π

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

• Vertical shift

• Horizontal shift

• Vertical stretch

• Horizontal stretch

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

• 2π

• π/4

• π/2

• π

In y = 2tan(4x), what is the value of the tangent function at the origin?

• 1

• 0

• 2

• Undefined

What is the shape of the tangent graph on the right side of the y-axis?

• Concave up

• Concave down

• Circular

• Linear

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

• Down π/4

• Up π/4

• Left π/4

• Right π/4

What happens to the asymptotes in y = tan(x - π/4)?

• Disappear

• Stay the same

• Shift right

• Shift left

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

• Vertical stretch

• Horizontal stretch

• Horizontal shift

• Vertical shift