2. Determine the amplitude, period and phase shift of the...

2. Determine the amplitude, period and phase shift of the function. Then graph one period of the function. Show your steps (basic graph and all transformations). Label each step. Don't forget to label the axes and show your scale. Four graphing templates are provided for your convenience. You may or may not need all of them. g(x) = - sin(2x - ?) Amplitude: Period: Phase Shift:

Transcript

00:01 So here we have the function g of x equals negative sign of 2x minus pi.

00:06 And what we want to do is determine its amplitude, period, and phase shift, and then graph one period of the function.

00:14 We're going to show our steps using our most basic graph and then all the transformations from there.

00:20 So the most basic graph in comparison to this one, its parent function, is g of that, i'll call it something different.

00:29 We'll say f of x equals sign of x.

00:34 Nothing fancy.

00:36 So f of x equals sign of x.

00:46 There you go.

00:47 Has an amplitude of one.

00:53 It has a period of 2 pi.

01:03 And there is no phase shift here.

01:05 So what that graph looks like is right here.

01:14 Again, that is a graph of an amplitude of one.

01:18 So from this midline, it goes up one and down one.

01:22 And the period is 2 pi.

01:23 So the length is from 0 to 2 pi.

01:27 And obviously, no phase shift has happened.

01:29 We haven't shifted left to right at all.

01:31 So what we want to take into account here is how g of x is different from f of x.

01:37 It is different first in that there is a negative out in front.

01:42 So when we determine our amplitude, that actually doesn't change anything, it's always the absolute value of a.

01:48 So our a value here being negative 1 still gives us an amplitude of 1.

01:55 So the height of this function is not going to change.

01:58 However, since it is a reflection, what will happen is each of these points will get reflected over the x -axis.

02:04 This first one being on the x -axis means that it is going to stay in the same exact spot...

Question

Please give Ace some feedback