It's a modification of sine function.
[tex]y = \sin(x)[/tex] - the first picture.
The values of y are in <-2, 2>. Therefore we have
[tex]y = 2\sin(x)[/tex] - the second picture.
The zeros of the function on the graph are 0, 2, 4, 6, ... → 2k, k ∈ Z
We know. The zeros of a sine are 0, π, 2π, 3π, ... → kπ, k ∈ Z
Therefore we have the equation:
[tex]2ka=k\pi[/tex] divide both sides by 2k
[tex]a=\dfrac{\pi}{2}[/tex]
Therefore your answer:
[tex]\boxed{f(x)=2\sin\left(\dfrac{\pi}{2}x\right)}[/tex]
