Amplitude

We first note the following modification to the trigonometric functions we have seen at this point. Consider the function . How is the graph of related to the graph of ? If we draw the two functions on the same set of axes, we obtain the following:

Note that this new function still has the same intercepts, but its range is now [-3,3] rather than [-1,1]. In essence, multiplication of the function by 3 has ``stretched'' the graph of vertically by a factor of 3, while retaining the same x-intercepts.

This vertical scaling factor is known as the amplitude of the function. Thus, in general, we say the following:

We now see how we can stretch a or function vertically. How would we shift it vertically? This is the subject of our next section.