Tangent Function Properties and Graphing

The video tutorial explains how to graph a transformation of the tangent function. It begins by discussing the properties of tangent as an odd function and how reflections affect its graph. The tutorial covers key properties such as amplitude, period, phase shift, and vertical shift. It provides a step-by-step guide to sketching the graph, focusing on the placement of vertical asymptotes and the shape of the graph. Finally, it addresses the domain and range of the tangent function, emphasizing the role of asymptotes in determining the domain.

What is the first step in graphing a transformation of the tangent function?

• Calculate the period

• Identify the vertical shift

• Factor the angle

• Determine the amplitude

Which property of the tangent function is not applicable?

• Amplitude

• Period

• Phase shift

• Vertical shift

How is the period of the tangent function determined?

• By multiplying the vertical shift

• By dividing the basic period by the leading coefficient

• By subtracting the phase shift

• By adding the leading coefficient

Where is the phase shift located in the tangent graph?

• At the right endpoint of the first period

• At the top of the graph

• At the center of the first period

• At the left endpoint of the first period

What is the role of vertical asymptotes in the tangent graph?

• They are at either end of the first period

• They mark the phase shift

• They indicate the vertical shift

• They determine the amplitude

How does a coefficient greater than one affect the tangent graph?

• It makes the graph wider

• It changes the period

• It makes the graph steeper

• It shifts the graph vertically

What happens to the tangent graph when there is a reflection?

• It shifts to the right

• It shifts to the left

• It goes steep and down to the right

• It becomes wider

What is the domain of the tangent function?

• Only negative numbers

• Only positive numbers

• All real numbers except where x is an asymptote

• All real numbers

How are consecutive asymptotes of the tangent function spaced?

• One unit apart

• Half a unit apart

• Three units apart

• Two units apart

What is the range of the tangent function?

• Only positive numbers

• Only negative numbers

• All real numbers

• Numbers between -1 and 1