Question

How do you find the amplitude, phase shift and period of `Y = 4 Cos 7πX – 7`?

Answer 1

The amplitude is always the number between the actual function. So in this case, the amplitude, or the number of units the graph moves up and down, is `4`.

`Y = 4 cos 7pi X - 7`

The phase shift, or the horizontal distance the graph moves from the original parent function, is always the value after `x`, so in this case, the horizontal shift is `- 7`.

The period of a `sin` or `cos` graph is always determined by taking the value of `2pi` and dividing it by the value before `x`. The period is the length of one cycle.

Period: `(2pi)/(7pi) = 2/7`

The raw value before `x`, `7pi` in this function, is identified as the cycle distance. This means that one cycle, or pattern of the graph, is `7pi` units long.