Characteristics of Tangent and Cotangent function

y-intercept of y=tan x

0

How many halfway points are there for each cycle in the tan function? What is the y-coordinate of the halfway point to the left? What is the y-coordinate of the halfway point to the right?

2; -1; 1

How many halfway points are there in the cot function? What is the y-coordinate of the halfway pint to the left? To the right?

2; 1; -1

domain of y=cot x

All real numbers except integer multiples of π

domain of y= tan x

All real numbers except odd integer multiples of π/2

Which one of the two functions is one-to-one?

Both

period of y=cot x

P=π

range of y= tan x

(-∞,∞)

range of y=cot x

(-∞,∞)

In the tan function, the x-coordinates of the center points are also the (complete the sentence)

x-intercepts, or zeros, and are of the form nπ where n is an integer

In the cot function, the center points are also the (complete the sentence)

x-intercepts, or zeros, and are of the form x=(2n+1)π/2 where n is an integer

The tan function has infinitely many vertical asymptotes with equations (complete sentence)

x= (2n+1)π/2

The cot function has infinitely many vertical asymptotes with equations (complete the sentence)

x=nπ where n is an integer

period of y= tan x

π

Is the graph even or odd; is the graph symmetric about the origin or about the y-axis?

odd; about the origin

Is the tan function even or odd? Is the graph symmetric about the origin or about the y-axis?

odd; symmetric about the origin