# Thread: Piecewise Function with Absolute Value fraction

1. ## Piecewise Function with Absolute Value fraction

Write h(x) into a piecewise function.

h(x) = 1 / |x - 1|

Read as: h of x equals one over absolute value x minus 1

My instructor also wrote x < 1, x > 1, and x = 1 on the side. Don't know what those mean though...

2. $\displaystyle h(x) = \frac{1}{|x-1|}$

at $\displaystyle x = 1$, $\displaystyle h(x)$ is undefined

for $\displaystyle x > 1$, $\displaystyle h(x) = \frac{1}{x-1}$

for $\displaystyle x < 1$, $\displaystyle h(x) = -\frac{1}{x-1}$

3. That's it? Nothing else?

I was writing it like this:
(1 / x - 1) > 1
(1 / -x + 1) < 1
1 / 0 is undefined

Nevermind, I think I understand...again.