# Vertical Shift of a Sine Function

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.

Interactive Tutorial

1. 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.

2. 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.

3. 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 |.

 a = 1 -10+10 b = 1 -10+10 c = 1 -10+10 d = 1 -10+10
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