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

where

__Interactive Tutorial__

- 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 |**.