Michael M. answered • 10/01/20
Struggling with STEM classes? I can help!
I believe that what this question is asking is this: Assuming that you have a graph of y=sin(x) (and I am assuming that most students are familiar with its shape). Now let a=1, b=1 and c=0. If we assign these three values to these three variables, then y=sin(x)=a*sin(b*x+c); that is, the graph of these two forms are identical.
Now, if we vary each of the variables (a,b and c), what effect is evident in the shape of the graph?
(a) If the value of a is increased, the sine graph is no longer limited to a maximum of y=1 and a minimum of y=-1, but is increased in the positive and negative y-direction (greater than 1 and less than -1); and if the value of a is decreased, the sine graph is decreased in the positive and negative y-direction (less than 1 and greater than -1).
(b) If the value of b is increased, the sine graph will no longer have x-intercepts at multiples of pi-radians, but will instead have x-intercepts that are farther apart (greater than pi); and if the value of b is decreased, the sine graph has x-intercepts that are closer together (less than pi).
(c) If the value of c is increased, the sine graph will no longer have x-intercepts at 0,pi,2*pi,etc., but instead will have x-intercepts offset from those numbers in the positive-x direction by an amount equal to the value of c; and if the value of c is decreased, the x-intercepts will be offset in the negative-x direction.
