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Graphing Trig Functions: Phase Shift (page 3 of 3)

Sections: Introduction, Examples with amplitude and vertical shift, Example with phase shift

• Graph two periods of g(x) = sin(πx + π/2) + 3

The amplitide is going to be the same, but the midline of the graph is going to be at y = 3 instead of y = 0 (that is, the x-axis). The period is going to be (2π)/(π) = 2. The argument factors as π(x + 1/2), so the graph will be shifted 1/2 unit to the left.

I'll do the usual graph: Copyright © Elizabeth Stapel 2010-2011 All Rights Reserved

Instead of shifting the sine wave three units up, I'll shift the horizontal axis three units down, and re-number the y-axis:

The regular period goes from 0 to 2π; this one goes from 0 to 2, so I'll re-number the x-axis:

And the graph is shifted to the left by 1/2, so I'll shift the y-axis to the right by 1/2  and re-number the x-axis a bit more:

Can you see why I used pencil and did a lot of erasing when I was doing graphing?

My best advice regarding doing these graphs is to practice, practice, practice. You don't want to freeze or have a "brain-fart" on the test, and this is pretty straightforward, once you get the feel of it. So keep doing extra graphing, until you are feeling comfortable and confident in your skills.

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