Question

How do you find the amplitude, period, and shift for `y=4tan2(x-pi/2)`?

Answer 1

• `"Amplitude" = abs(a) = 4`
• `"Period" = pi/b = pi/2`
• `"Phase Shift" = c/b = pi/2`

Explanation:

Here's one way to write a generic tangent function that has been transformed in some way.

`f(x) = atan(bx-c) + d`

In this scenario:

• `"Amplitude" = abs(a)`
• `"Period" = pi/b`
• `"Phase Shift" = c/b`

For your specific problem, the coefficient `b` has already been factored out, meaning the problem is a bit easier:

`f(x) = atan(b(x-c/b)) + d`

The values are identical, but a bit easier to spot:

• `"Amplitude" = abs(a) = 4`
• `"Period" = pi/b = pi/2`
• `"Phase Shift" = c/b = pi/2`

If this function was a sine or cosine function, the period would be `(2pi)/b` instead.