How do I graph y= -2tan x and having it show 2 cycles along with finding the domain and range?

Answer 1

For this question, you will want to know the transformations and the normal period of Tangent.

y=a tan b(x−c)+d

Where |a| is the amplitude, how far up/down the graph goes from the middle, think Stretch if a>1 or Compression if a<1

b is the number of times the graph will repeat itself in the normal period (this is π for tan).

c is the horizontal phase shift, notice it is inside the parentheses (right if negative, left if positive)

d is the vertical shift, notice this is outside the parentheses.

For your problem:

y = -2tanx

1. amplitude is stretched vertically by a factor of 2, and reflected (because of the negative) around the X axis.
2. no phase shift or vertical shift, and the period is normal at π
3. The domain (allowed x values: tan x is undefined at every π/2) so domain: all real numbers except π/2 + nπ
4. range: y values which are defined from -∞ to + ∞

To plot, just enter degrees into the equation (say -30, 0 and +30, or -π/6, 0, π/6 for radians) and you will see the pattern repeat as well as the asymptotes.

I hope this helps!