Question

What is the period of the function f(x) shown in the graph?

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Basic

Answer 1

Period is
`\mbox{\huge {\boxed{\pi }}}`

Explanation:

Each gridline marker on the horizontal axis is π/4

The period of this function is the horizontal displacement at which the function starts to repeat itself

Looking at the function we see that the minimum value of the function is 1 and occurs first at -π/4 and then at 3π/4

So the period is 3π/4 - (-π/4) = 3π/4 + π/4 = (3/4 + 1/4)π = π

We could also double check this using another point of reference

let's take the peaks of the function
The first peak visible is at -3π/4 and the next peak at π/4

So the period = π/4 - (-3π/4) = π/4 + 3π/4 = π