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Keep in mind that the x-axis will most likely be in Radians, if not it will be in Degrees.
A vertical translation is a shift in a graph up or down along the "y" axis, generated by adding a constant to the original function.
Hint: Vertical means upright, or going up and down. The "y" axis is upright also
This is what a vertical translation would look like on a graph but in a function you would have to add or subtract by a number depending if you want to shift the graph up or down.
This is the same as a vertical translation only that it shifts the graphs left or right
Caution: When shifting the graph, keep in mind the subtraction or addition sign, these depict whether the graph shifts to the left or to the right. If there is a negative sign then the graph shift to the left but if there is a positive sign then then the graph shifts to the left!
The amplitude of a wave is a measure of the wave's height.
Tip: For the image above, the center line is at y=0 and the amplitude affects the height above and below that line by two!
How can the range be affected by changing the amplitude?
Period and Frequency
The period of a wave is the horizontal distance traveled before the 'y' values begin to repeat.
TIP: just remember that the period is when the the values will repeat again.
Since the period and frequency is inversley related, what happes to the period as the frequency increases? Click here for guidence.
Tip: Always start with the vertical translation and then horizontal translation so that it makes the graphing much easier.