Question

How do you find the amplitude, period, and shift for `y=4tan(2x-pi)`?

Answer 1

The amplitude is 4, the period is `pi/2`, and the graph is shifted to the right `pi/2`.

Explanation:

The general pattern for a tangent function is:
`y=atanb(x-h)+k`

In this case, `a` is 4, so the amplitude is 4.

To find the period, we need to find the `b` value first. To do this, we need to pull out the 2 in order to isolate `x`. Therefore, we get:
`y=4tan2(x-pi/2)`
The period for a tangent function is equal to `pi/b`.
`pi/b=pi/2`

The `h` value is how much the graph is shifted horizontally. In this case, we can see that the graph is shifted to the right `pi/2`.