# is f: x → |x| a function of x?

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• June 3rd 2010, 08:03 AM
Savior_Self
is f: x → |x| a function of x?
"Determine whether or not the mapping of f: x → |x| is a function of x and explain your answer."

Hey, this is a question on a calculus worksheet I've been given that I've never seen before in the book and I'm not entirely sure of how to answer this. If someone could point me in the right direction, I'd appreciate it. Thanks.
• June 3rd 2010, 08:06 AM
Defunkt
How did you define a function in your class notes? Does $f : x \mapsto |x|$ answer that definition?
• June 3rd 2010, 08:47 AM
Savior_Self
Quote:

Originally Posted by Defunkt
How did you define a function in your class notes? Does $f : x \mapsto |x|$ answer that definition?

My problem is I don't really understand the notation..

I know that an input value of a function cannot have two different output values..

Is this notation telling me that there are two different outputs for a single input?
• June 3rd 2010, 08:53 AM
Unknown008
This notation is the same as:

$f(x) = |x|$

if this helps.

You should know the shape of the graph of y = |x|
• June 3rd 2010, 09:09 AM
undefined
Quote:

Originally Posted by Savior_Self
"Determine whether or not the mapping of f: x → |x| is a function of x and explain your answer."

Quote:

Originally Posted by Defunkt
How did you define a function in your class notes? Does $f : x \mapsto |x|$ answer that definition?

Just so you're aware, the difference in arrows is important. Defunkt's arrow is correct, but your arrow means something else. (And I realize it can be hard to type in.)

Your arrow specifies domain and range. So, a complete definition of f could look like this:

$f:\mathbb{R}\to \mathbb{R} : x \mapsto |x|$