Having trouble graphing a log with absolute value of x .

Question

y= log₂|X| 

 

I really need to be guided through this with details. The first I did was attempt to do a table of values for y=log₂(X) and y=log₂(-x)

 

Both tables are giving the same set pf points so clearly im  doing something wrong. 

 

 

UPDATE: I just figured how to do it. Only question I hqve is for the asyomtotes( i forgot how to spell it lol) , would it be x=0 for both ? 

 

Answer 1

Yes, Alex, the vertical asymptote for both + and - is x = 0, no horizontal asymptote.

Answer 2

Since the argument x is an absolute value, we can ignore the negative numbers for now (due to the fact that the absolute value of any number is always positive.  So you can write the function as

 

y = log₂(x)

 

 

This function can be written as

 

2^y = x

 

 

Since our base is positive, x>0.

 

If the domain starts and zero, then y would be all real numbers.

 

 

Lets pick points to test out.

 

2^-5 = 1/32

 

2^-4 = 1/16

 

2^-3 = 1/8

 

2^-2 = 1/4

 

2^-1 = 1/2

 

2⁰ = 1

 

2¹ = 2

 

2² = 4

 

 

From these test points, x increases as y increases.  Plot the points (x, y) using the test points.  Then connect the point in the pattern they follow.  Then once you have your curve, you will reflect that curve over the y-axis.

 

 

Your vertical  asymptote occurs at x=0  because there is no number when raised to any power that will give a result of zero.

 

 

Does this all make sense to you?