Consider the general form of a transformed sine function, y=asin b(x-h)+k.
Practice makes perfect
Let's consider the given function.
y=sin (x-π)+4
Now we will compare our function with the general form of a transformed sine function.
General Form
y= a sin b(x- h)+ k
Given Function
y= 1 sin 1 (x- π)+ 4
Because a= 1 and b= 1, the desired graph is a translation of y=sin x. Since k= 4, the graph of the given function translates the graph up by 4 units. The horizontal translation of a periodic function is called a phase shift. Therefore, h= π tells us that there is a phase shift of π units to the right.
Finally, we will draw the obtained graph in the interval from 0 to 2π. We will extend the current pattern to 0 and restrict the domain to values of x that are not greater than 2π.
