4e Example 2 (How to Graph the Tangent Function Part 1)

The video tutorial explores the tangent function, highlighting its similarities and differences with sine and cosine functions. It covers key characteristics such as period, phase shift, and vertical transformations. The tutorial also delves into graphing the tangent function, identifying asymptotes, and understanding reflections and vertical stretches. Algebraic methods for solving asymptotes are demonstrated, providing a comprehensive understanding of the tangent function's behavior.

What is a key difference between the tangent function and sine or cosine functions?

• Tangent is always positive.

• Tangent has a maximum value.

• Tangent has vertical asymptotes.

• Tangent has an amplitude.

How is the period of the tangent function determined?

• π/B

• B/2π

• 2π/B

• B/π

What is the vertical shift in the tangent function if the graph is moved up by 3 units?

• Right 3 units

• Left 3 units

• Up 3 units

• Down 3 units

Where do the vertical asymptotes of the tangent function occur?

• At the maximum points

• At the minimum points

• At the midpoint of each period

• At the start and end of each period

What happens to the tangent graph when it is reflected about the x-axis?

• It shifts up.

• It flips horizontally.

• It shifts down.

• It flips vertically.

How does a vertical stretch affect the tangent graph?

• It shifts the graph right.

• It makes the graph wider.

• It shifts the graph left.

• It makes the graph narrower.

What is the effect of a negative sign in front of the tangent function?

• It reflects the graph about the x-axis.

• It reflects the graph about the y-axis.

• It shifts the graph up.

• It shifts the graph down.

How do you find the new asymptotes after a transformation?

• By dividing the period by the original asymptotes

• By multiplying the period by the original asymptotes

• By subtracting the period from the original asymptotes

• By adding the period to the original asymptotes

What is the domain of the tangent function?

• Only positive numbers

• Only negative numbers

• All real numbers except where asymptotes occur

• All real numbers

How do you solve for x in a tangent equation?

• Set the equation to one

• Set the equation to a maximum

• Set the equation to an asymptote

• Set the equation to zero