Question from Rachel:
Question involving absolute value in Algebra 2: 3.4.
Example 5 on page 233 states that “If X<0, then |x| = -x.
That really confused me. I thought that absolute value was just that – absolute! There are not supposed to be any negatives involved, right?
But obviously, there are, and I’m not sure why. I’d appreciate some help. Thank you!
Answer from Dr. Callahan:
I know it looks confusing – but note that they are NOT saying |x| = -x — but instead they are looking for a trick to help break up the complex function into pieces.
See top of page 232.
This is saying that anytime you have a function with absolute value – you know it is likely to be a piecewise function – in other words it will break somewhere like this one does
So this replacement is mostly a trick to make it work.
For instance – think about breaking up
y = |x| into piecewise.
It looks like this
To find this we let |x| = x when x>=0 and then |x| = -x when x<0. This swaps the signs for you – a trick. Try it by making a table of x and y for value positive an negative of y = |x|.
So again – this is more a trick to break it up than a FACT. See in the example right next the the word SOLUTION is says we are trying to break this up into a form that does NOT involve |x|.