Absolute Value

Consider the following.

On graph paper, sketch the graph of y = |x| + 2. What do you think would happen if you change the 2 to -2? Sketch the graph of y = |x| -2 to see if you are correct.
On graph paper, sketch the graph of y = |x + 2|. What do you think would happen if you change the 2 to -2? Sketch the graph of y = |x - 2| to see if you are correct.

How does the graph of y = |m|x differ from y = |mx|?
How are the graphs of y = |m|x , y = |mx| and y = m|x| similar? How are they different?
How does the graph of y = |mx| differ from y = |mx| + b as b varies?
How does the graph of y = |mx| differ from y = |mx +b| as b varies?
What happens to the graph of y = |ax²| +bx + c as a, b, and c vary (including positive and negative numbers)?
What happens to the graph of y = |ax² +bx| +c as a, b, and c vary (including positive and negative numbers)?
What happens to the graph of y = |ax² + bx + c| as a, b, and c vary (including positive and negative numbers)?
How are the graphs of y = |ax²| +bx + c, y = a|x²| +bx + c , and y = |a|x² +bx + c similar? How are the different?
How are the graphs of y = ax² +|b|x + c, y = ax² +|bx| + c , and y = ax² +b|x| + c similar? How are the different?
How are the graphs of y = ax² +bx + c, and y = ax² +bx + |c| similar? How are the different?