Question

what is the equation for the following graph

Answer 1

So the first thing to notice is that it oscillates, which tells you that it has to be sin or cos.

The second thing we see is that it's got a non zero value at zero, so it's cos.

Next we can see that it's been stretched. The normal range for cos is -1 to 1, so 1+1 = 2.

However, the range here is 4.

So we multiply cos(x) by 2 to get 2cos(x)

And finally, we can see that the entire thing has been shifted upwards by a value of one

So your final equation is 2cos(x) + 1