We have been given graph of a sinusoidal function. We are asked to write function formula for our given graph.
We know that and
. We can see that our given function is starting at origin, so our graph is sine function.
We know that general form of sine is , where,
A = Amplitude,
Period:
C = Horizontal shift,
D = Vertical shift.
We have been given that function has no horizontal shift, so the value of C is 0.
We can also see that midline of our function is x-axis, so there is no vertical shift as well that is .
We can see that function goes up to 1 from midline and goes down to from midline, so amplitude of function is 1 that is
.
We can see that period of our given function is because it completes one cycle from
to
We can see that our function is reflected about x-axis, so our function will be .
Therefore, our required function is .