# Thread: Graphing absolute-value functions

1. ## Graphing absolute-value functions

How do i graph absolute value function with x^2?

f(x) = |x^2 - 2|

What happens or how does it move if changing f(x)m for example - f(x), f(x+3), f(x) + 3 ??

Anybody who knows a good website that explains this?

Thanks

2. ## Re: Graphing absolute-value functions

Originally Posted by ronaldopeter
How do i graph absolute value function with x^2?

f(x) = |x^2 - 2|

What happens or how does it move if changing f(x)m for example - f(x), f(x+3), f(x) + 3 ??

Anybody who knows a good website that explains this?

Thanks
To plot the modulus of a function reflect any negative part of f(x) in the x axis.

In your example reflect the portion between $(-\sqrt{2},0) \text{ and } (\sqrt{2},0})$ in the y axis

$|f(x)|+a$ is moving the graph by a on the y axis. It can go negative if a is sufficiently negative

$|f(x+h)|$ is a translation of f|x| on the x axis.

$a|f(x)|$ can be +ve or -ve depending on the value of a.

For example $-|f(x)| \leq 0$

edit: for your example see these wolfram alpha plots

3. ## Re: Graphing absolute-value functions

Originally Posted by ronaldopeter
How do i graph absolute value function with x^2?

f(x) = |x^2 - 2|

What happens or how does it move if changing f(x)m for example - f(x), f(x+3), f(x) + 3 ??
it's called transformation of functions ... try a google search.

f(x) , -f(x) , f(x+3) , f(x) + 3