Question

To get a better look at the graph, you can click on it.

Find a function of the form f(x)=A sin(B[x−C])+D whose graph is the sine wave shown above. The curve goes through the points (−5,0) and (1,0).
If needed, you can enter π=3.1416... as 'pi' in your answer.

f(x)=

Answer 1

There are many curves which go through those two points.
Lat's make it easy and say that we have a sine curve of period 12, crossing the x-axis at the two points. That means we have one arch of the curve (1/2 period).
If we pick (-5,0) as our starting point, then
f(x) = sin(π/12 (x+5))
That gives us A=1 and D=0
I'll let you decide whether you want to complicate things, such as, what if D is not zero?