Question 169368
: I have come to a point in solving : is this function one-to-one, where the absolute value of a = the absolute value of b. Can this be one to one? 
For the record, the problem states: f(x)= |x| - 2 
I assigned a and b, and equal them to each other. 
|a| - 2 = |b| - 2 ; add two to both sides 
|a| = |b| 
therefore a = b? or not really? 
<pre><font size = 4 color = "indigo"><b>
No it does not! for instance we could take a=3 and b=-3, then

|3| = |-3|

Another way to say it is it's not one-to-one because,
for instance f(3) = f(-3) =  1 but 3 does not equal -3.   

The points (3,1) and (-3,1) are both on the graph and
a horizontal line goes through them both, so the graph does not pass the horizontal line test.

The graph looks like this:

{{{drawing(400,400,-5, 5, -5,5,
graph(400,400,-5,5,-5,5,abs(x)-2))}}}

And as you see, the horizontal lines cut it more than
once, so it cannot be one-to-one.

{{{drawing(400,400,-5, 5, -5,5,
graph(400,400,-5,5,-5,5,abs(x)-2),
line(-6,2.7,6,2.7), line(-6,1.85,6,1.85), line(-6,1,6,1),line(-6,pi,6,pi),
line(-6,-1,6,-1),line(-6,1.5,6,1.5) )}}}

Edwin</pre>