The following exercise will could be very useful to anyone who missed class when we discussed how the values of a, h & k affect the graph of
y=a|x-h|+k when these values change.

Part One - Going to the Grapher Tool and Graping f(x)=a|x-h|+k
You will need to go to the Grapher tool described in the video below. If you feel brave, you can just click the here and go to it. However, the video below gives a little bit of description about the the graphing tool works. So, it might be useful.

Once you are there, please enter a|x-b|+c in the graphing window and hit the Graph button. Before you go any further, use the sliders to make sure that a=1, h=0 and k=0. Note that a is the same that we used in class with our notes. The Grapher tool does not allow us to use the letters h & k. So, just use b instead of the letter h and c instead of the letter k. Just know that everytime we say b here we mean h and everytime we say k here we mean c.

This video describes how to access a graphing tool that allows you to recreate the Sketchpad Demo that I did in class without the sketchpad document. It uses an internet based graphing tool that works in a similar fashion. Feel free to message and post discussion around using it. It might be neat to use it to check this assignment.






Part Two-Seeing How the Value of "h" Affects the Graph of y=|x|
The following questions will help you "play along" with the notes found on slide 6 of the notes from class for this lesson. Click here to get them.

1. If you need to, move the sliders so that a=1, h=0 & k=0.

2. Pick a positive value for h. Move the slider so that h (in this case b) becomes that value? How did this "TRANSFORM" the graph?

3. Form a hypothesis about how the graph will change when you pick a negative value for h (in this case b). Move the slider so that h (in this case b) becomes that value? How did this "TRANSFORM" the graph?

4. What value would h have to be for the graph of y=|x| to slide horizontally -4 units?



Part Three-Seeing How the Value of "k" Affects the Graph of y=|x|
The following questions will help you "play along" with the notes found on slide 6 of the notes from class for this lesson. Click here to get them.

1. Move the sliders so that a=1, h=0 & k=0.


2. Pick a positive value for k. Move the slider so that k (in this case c) becomes that value? How did this "TRANSFORM" the graph?

3. Form a hypothesis about how the graph will change when you pick a negative value for k (in this case c). Move the slider so that k (in this case c) becomes that value? How did this "TRANSFORM" the graph?


4. What value would k have to be for the graph of y=|x| to slide vertically 2.5 units?



Part Four-Seeing How the Value of "a" Affects the Graph of y=|x|
The following questions will help you "play along" with the notes found on slide 7 of the notes from class for this lesson. Click here to get them.

1. Move the sliders so that a=1, h=0 & k=0.

2. Pick a a value for a such that a>1. Move the slider so that a becomes that value. How did this transform the graph?

3. Pick a positive value for a that is less than 1. (I.e. 0<a<1). Move the slider so that a becomes that value. How did this transform the graph?

4. Move the slider so at a=-1. How did this transform the graph?

5. Form a hypothesis about what will happen if a=-3. Move the slider so that a becomes equal to -3. Was your hypotheses correct?