Question

How do you find the amplitude, period, and shift for `y=3tanx`?

Answer 1

amplitude: N/A
period: `180^@`
phase shift: `0`

Explanation:

amplitude: how far the graph extends from its midline

e.g. the amplitude of `y = sin x` is `1`, since the midline is `y=0`, and the highest and lowest points are `1` and `-1`.

the amplitude of `y =3 sin x` is `3`, since the midline is `y=0`, and the highest and lowest points are `3` and `-3`.

however, the `tan x` graph does not have a certain amplitude.

`tan 90^@` is undefined. without knowing the highest point on the graph, the distance that the graph extends from the midline cannot be calculated.

period: how often the values of the graph repeat themselves

`3 tan 0^@ = 0, 3 tan 180^@ = 0`

`3 tan 45^@ = 3, 3 tan 225^@ = 3`

`180^@ - 0^@ = 180^@`
`225^@ -45^@= 180^@`

this means that the values of `tan x^@` on the graph recur every `180^@`.

phase shift: how far to the right a wave is from its usual position.

usual position of `y=tan x`:

graph{tan x [-10, 10, -5, 5]}

`y = 3tanx`:

graph{3tan x [-10, 10, -5, 5]}

the graph has not been moved in either horizontal direction - the values for both at `x=0` are both the same.