graph y=3-2sinx for 0<x<2pi

Question

start with graph of parent function sin x, then use transformation rules to complete it. label the function and transformation name on each step.

Answer 1

Start with the parent function y = sin(x) which looks like the red dotted line. The negative in front of the sine reflects it over the x-axis to give you the blue dotted line. The number 2 in front of the sine stretches the graph by a factor of 2 in the y direction to give you the solid blue line. The 3 moves the entire graph up 3 units to give you the final graph in the solid black line.