How do you graph  y=-1+tan2x?

To graph $y = - 1 + \tan 2 x$, we determine the x and y intercepts and then add points that will enable to draw graph for 1 period. See the explanation.

Explanation:

The given equation

$y = - 1 + \tan 2 x$

Set $x = 0$ then solve for $y$

$y = - 1 + \tan 2 x$

$y = - 1 + \tan 2 \left(0\right)$

$y = - 1$
We have the y-intercept at $\left(0 , - 1\right)$
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Set now $y = 0$ then solve for $x$

$y = - 1 + \tan 2 x$
$0 = - 1 + \tan 2 x$

$1 = \tan 2 x$

$\arctan \left(1\right) = \arctan \left(\tan 2 x\right)$

$\frac{\pi}{4} = 2 x$

$x = \frac{\pi}{8}$
We have the x-intercept at $\left(\frac{\pi}{8} , 0\right)$

Other points are $\left(\frac{\pi}{4} , + \infty\right)$ and $\left(- \frac{\pi}{4} , - \infty\right)$

Since the graph of $y = - 1 + \tan 2 x$ is periodic, there will be a repetition of the same graph every $\frac{\pi}{2}$ period. Kindly see the graph of $y = - 1 + \tan 2 x$