a monitor displays the graph y = sin 5x. what will be the amplitude after a dilation of 2?
To find the amplitude after a dilation of 2, we need to understand what a dilation does to a graph.
A dilation is a transformation that stretches or compresses a graph. In this case, we want to dilate the graph of y = sin 5x by a factor of 2.
The general formula for a dilation of a function is: y = a * f(x), where a is the dilation factor.
In the given function y = sin 5x, the amplitude is 1, since the amplitude of the basic sine function is always 1.
To find the new amplitude after the dilation by a factor of 2, we multiply the original amplitude by the dilation factor (2):
new amplitude = original amplitude * dilation factor
= 1 * 2
= 2
Therefore, after the dilation of 2, the new amplitude will be 2.