Tangent Functions

What is the period length of y=tanx

• π

• 2π

• -2π

• π+1

What are the vertical asymptotes for y = tan(x)?

• x = ... pi/2, 3pi/2, ....

• x = ... 0, pi, 2pi, ....

• There are no vertical asymptotes.

• x = infinity, x = - infinity

Graph

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Graph

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Determine an equation for this graph:

• y=csc(x)

• y=sec(x)

• y=cot(x)

• y= tan(x)

Sketch a graph of the parent tangent function, y = tan a. Describe the domain, range, symmetry, period, and any asymptotes of the graph.

b

c

d

e

a

Point symmetry (odd)

All angle measures except 90, 270, etc

All angle measures

Which graph matches the equation?

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Describe the transformation from the parent function of tan(x).

• Vertically compressed by 2 and vertical shift down 1

• Vertically compressed by 2 and horizontal shift right 1

• Vertically stretched by 2 and vertical shift down 1

• Vertically stretched by 2 and horizontal shift right 1

What is the equation of the graph shown?

• y = tan θ

• y = sin θ

• y = cos θ

• y = -5tan θ

What is the value of a if the function above is f(x) = a tan x

• 1/2

• 1

• 2

• 4