How would I grapg this logarithm if the x is absolute ?

Question

y=log₂ |x| 

 

I dont understand because wouldnt there be two graphs for this instead of one? Also, if i were to find the table of values , what would it be ? 

Answer 1

Regardless of whether you substitute a positive number or a negative number in place of x, its absolute value will be used, so you'll be using the log (base 2) of a number > 0.  So you just graph the normal log₂x, where x>0, and then you reflect it ALSO in the y-axis. The graph has two unconnected parts, one in quadrant 1, the other in quadrant 2. Note x≠0.

 

The table of x values would be ±1, ±2, etc... and the associated y values would be 0, 1, etc.