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09-13-2010   #1 (permalink)
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Default Absolute value/Piecewise function

f(x) = 3|x-2| - |x+1|

f(x) = x+2|x+1| / x+1

Write a piecewise definition for f and sketch the graph of f.

Last edited by evilxshadow; 09-13-2010 at 07:03 PM.
 
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09-13-2010   #2 (permalink)
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Quote:
Originally Posted by evilxshadow
f(x) = 3|x-2| - |x+1|

f(x) = x+2|x+1| / x+1

Write a piecewise definition for f and sketch the graph of f.
Any kind of piecewise function? Could just make it so the first equation is for a domain from (-inf., -1] and the second is from (-1, inf.). Graphing would depend on however you decide to put together a piecewise function. And for that, you should just be able to plug in numbers and graph that way. No need for anything fancy when you can make it super-simple. Just be sure to note that the -1 value for the second equation has an open circle; no value exists because it is not in the domain.
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09-13-2010   #3 (permalink)
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An alternate way to graph is to find the critical points (x={-1,2} for the first, and x=[-1] for the second) then mapping where point itself and points to the left and right go.

After you do a bunch more of these, you won't have to do that. But it's a little easier to do this if you havn't done tons of these before.
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