Answer:
f(x) = 2cosx + 1
Step-by-step explanation:
We first want to make it "symmetric" to the x-axis, so we look at the maximum and minimum y-value. We see that the maximum value is 3 and the minimum value is -1. For making it symmetric we'll move this graph along the y-axis so it will have a maximum of 2 and a minimum of -2. We then notice that when x=0, y=2, meaning that it is a cos function, as the y is maximum when x=0, if not moved to the right or left). We also know that the maximum value of the y-axis for a cos function is 1, while the minimum is -1. That translates into a cos graph stretched along the y-axis: y=2cosx. But let's not forget that at the beginning we have moved the graph along the y-axis by 1 unit, so we have to move it back now: y=2cosx + 1.
I hope it's clear. Tried to make it as easy as possible to understand. Sorry for my poor English.
