Absolute value functions graphing: How can you tell by the equation if the graph flips upward, shifts to the right or left, or moves upwards?

Question

I am really confised and need help because I have a test tomorrow.

Answer 1

To determine if the graph flips upward, we simply negate the absolute value.

 

y = | x + c |   and    y = | x - c |  ------>  upward

 

y = - | x + c |   and    y = - | x - c |  ------>  downward

 

 

To determine if the graph shifts to the right or left:

 

y = | x + c |  ----> shifts to the left

 

y = | x - c |  -----> shifts to the right

 

where c is a constant. 

 

 

Keep in mind: the signs in front of the absolute value symbol does not matter in a shift. 

 

 

Feel free to use a graphing calculator to experiment.