Practice!

Sample Problem

 

What is the function of this graph?

g(x)= + sin(x)

Solution

This looks like the sin x graph vertically shifted upward 2 units so there should be a plus 2 outside the sin function. The period of this graph is π, which means that b in sin bx=2. (Period=2π/b → π=2π/b → b=2). Finally, the amplitude of this graph (that is, half the distance between the maximum value (5) of this function and the minimum value (-1)) of this function is 3. Therefore, the a in asinbx is 3. The function should look like

g(x)=2+3sin2x