Question

How do you find the amplitude and period of a function `y=3 tan (4x-pi/3)`?

Answer 1

The amplitude is 3, and the period is (`pi`/4).

Explanation:

All tangent functions take the form of the following:
y = a tan b x

The variable a is the amplitude (max-min/2; the length above and below the x-axis the graph goes), the variable b represents the amount of cycles (a cycle is one pattern that is repeated in the function), and x is the variable that stays unknown when graphed (unless when being solved for by graphing).

To find the amplitude, simply look at a. In this case, the amplitude is 3, since it is the number before tan and takes the spot of a.

To find the period, divide `pi` by b (`pi`/b = period). Find your b value, and put `pi` over it, like so: `pi`/4. 4 is b in this example, and since there is no way to simplify that, the period is `pi`/4.
(Hint: use the expression `pi`/ b)

Hope this helped! :)