absolute values and describing the change

Question

describe how the graph of the following absolute value equation is effected by the given change  y=[x] and y=-2[x]

Answer 1

Do you mean the change from y=[x] to y=-2[x]?

 

The graph of the absolute value function is V shaped.  A line (actually a "ray") of slope 1 goes up and to the right from the origin (0,0), and a ray of slope -1 goes up and to the left from the origin.

 

When changing to the second function, there are two differences.  First of all, the values of the function are all negative instead of positive.  So the ray going up and to the right now would change to go DOWN and to the right.  And the ray going up and to the left would change to go down and to the left.

 

The other change is that instead of a slope of 1 or -1, the rays would have slopes of 2 or -2.  So the rays from the origin would be steeper.  So what you would have is an upside-down V with steeper sides.