How do you graph $y = - tan 2 x$ $y=-tan2x$ and include two full periods?

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How do you graph $y = - tan 2 x$ $y=-tan2x$ and include two full periods?

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Answer 1 · 2017-03-20T22:57:34

Create a normal tan graph:
graph{tan(x) [-0.5, 6.29, -4, 4]}
(If you don't know how, then either think of how tan changes as the angle of the triangle increases from zero, or remember this chart:

$0$ $0$ : $0$ $0$
$\frac{π}{4}$ $pi/4$ : $1$ $1$
$\frac{π}{2}$ $pi/2$ : undefined (goes off to infinity)
$\frac{3 π}{4}$ $(3pi)/4$ : $- 1$ $-1$
$π$ $pi$ : $0$ $0$
Repeat this at least twice.)

Then compress it in the horizontal by a factor of two (because of the $2 x$ $2x$ in the tan:
graph{tan(2x) [-0.5, 6.29, -4, 4]}
Then flip it on the vertical (because of the negative sign):
graph{-tan(2x) [-0.5, 6.29, -4, 4]}

The graph must show at least $π$ $pi$ , since the period of $tan (x)$ $tan(x)$ is pi, which was divided in two by the 2x inside the tan, then multiplied because you need to show two periods

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How do you graph $y = - tan 2 x$ $y=-tan2x$ and include two full periods?

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