Question

Find the formula for the graph of function f(x) given in the graph above

Answer 1

This is a sin function since for x = 0, y = 0

The general formula of such functions is:

f(x) = A sin (bx + c) + d, where:
A= period
b = coefficient of x
c= phase shift (horizontal shift)
d= vertical shift

Since there is no vertical shift nor horizontal shift, our function becomes:

f(x) = A. sin(b.x)

In the graph we notice that A=2
Let's calculate b. Remember that the PERIOD = 2π/b, but the period given on the graph is 8π, then:
:
8π = 2π/b → and b= 2π/8π → b= 1/4

Finally the equation is : f(x) = 2.sin(x/4)