Precalc question

Question

Graph: 𝑦 = |3cos(2𝑥 + 𝜋)| 4

what would the amplitude, period and five points?

Answer 1

I think the answer to the amplitude is a bit debatable. Typically, the definition of amplitude of cyclical functions like sine and cosine is defined as the distance from the equilibrium point or "center line" of the graph to the peak. Sometimes it's defined as max-to-min divided by 2. In this function, the graph has only a positive movement away from what would typically be called it's center line. So to use the tact of taking the high point and low point and averaging them seems incorrect to me. I would call the amplitude the distance from the bottom to the top or "3". That is the way electrical engineers typically define the amplitude of things like this (such as a square wave).

The period is the x-value distance from one cycle to the next. In this case the function repeats every π/2 units so the period is π/2.