Tangent Function Transformations and Properties

The video tutorial explains how to graph the function y = tan(2x - π). It emphasizes understanding the parent function and identifying transformations such as period, X scale, and phase shift. The instructor guides through calculating these elements and graphing the function, highlighting common student errors and misconceptions.

What is the first step in graphing the tangent function?

• Understand the parent function

• Calculate the reflection

• Identify the amplitude

• Determine the vertical shift

How is the period of the tangent function calculated?

• 2 Pi divided by the coefficient of x

• Pi times the coefficient of x

• 2 Pi times the coefficient of x

• Pi divided by the coefficient of x

What is the X scale for the function y = tan(2x - π)?

• Pi

• Pi/2

• Pi/4

• 2 Pi

What is the phase shift for the function y = tan(2x - π)?

• Pi/2 to the right

• No phase shift

• Pi/4 to the left

• Pi/4 to the right

What is the vertical transformation for the function y = tan(2x - π)?

• Shifted up by 2

• No vertical transformation

• Shifted down by 1

• Shifted up by 1

Where does the tangent function typically cross the x-axis?

• At 2 Pi

• At 0

• At Pi/2

• At Pi

What is the distance between each X scale in the modified tangent function?

• Pi

• Pi/4

• 3 Pi/4

• Pi/2

How does the phase shift affect the starting point of the tangent graph?

• It changes the starting point on the x-axis

• It reflects the graph

• It shifts the graph down

• It shifts the graph up

What is the correct interpretation of the transformation in the function y = tan(2x - π)?

• Shifted right by Pi/4

• Shifted left by Pi/2

• Shifted right by Pi/2

• Shifted left by Pi/4

Why is it important to understand the parent graph of the tangent function?

• To calculate the period

• To identify the correct transformations

• To determine the amplitude

• To find the vertical shift