What is the vertical shift of a sine function? An interactive tutorial using an html 5 applet to investigate the vertical shift of a sine function of the form
f(x) = a sin(bx + c) + d
where a, b, c and d are real numbers and a not equal to zero, is presented.
Press the button 'draw' on the left panel below. Two graphs are shown: a red one corresponding to the function h(x) = a sin(b x + c) and a blue one corresponding to the function f(x) = a sin(b x + c) + d.
Use the slider to change the value of d (you may also enter values in the box for d). Only the blue graph is shifted up or down depending whether d is positive or negative.
Keep a, b and c constant and change d using the slider or entring values in the box for parameter d then press the button 'draw'. For each value of d selected, verify that the maximimum value of function f(x) = a sin(b x + c) + d (blue graph) is equal to d + | a | and its minimum value is equal to d - | a |.