# Graph this piecewise function and use it to determine the values of a for which the l

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• September 27th 2010, 09:45 PM
iamanoobatmath
Graph this piecewise function and use it to determine the values of a for which the l
$\begin{displaymath}
f(x) = \left\{
\begin{array}{lr}
2-x & if x<-1\\
x & if -1<=x<1\\
(x-1)^2 & if x>=e1
\end{array}
\right.
\end{displaymath}$

I'm supposed to graph this piecewise function and use it to determine the values of a for which the limit of f(x) exists as x approaches a.

http://www2.wolframalpha.com/Calcula...21&w=399&h=188
I'm not entirely sure how to start this question. Looking on the graph I'm thinking the only place where the limit of f(x) as x approaches a doesn't exist is -1 and 1. Could someone please explain? (Worried)
That is the graph. So does the limit of f(x) as x approaches a exist everywhere except 1 and -1 ?(Worried)
• September 27th 2010, 09:54 PM
undefined
Quote:

Originally Posted by iamanoobatmath
$\begin{displaymath}
f(x) = \left\{
\begin{array}{lr}
2-x & if x<-1\\
x & if -1<=x<1\\
(x-1)^2 & if x>=e1
\end{array}
\right.
\end{displaymath}$

I'm supposed to graph this piecewise function and use it to determine the values of a for which the limit of f(x) exists as x approaches a.

http://www2.wolframalpha.com/Calcula...21&w=399&h=188
I'm not entirely sure how to start this question. Looking on the graph I'm thinking the only place where the limit of f(x) as x approaches a doesn't exist is -1 and 1. Could someone please explain? (Worried)
That is the graph. So does f(x) exist everywhere 1 and -1 (Worried)

Well, f(x) is defined over all the reals, but $\displaystyle\lim_{x\to a}f(x)$ does not exist at a=-1 and a=1 as you said. There's really not a lot to it. (If you want some more detail: at those points left and right limits exist, but they are not equal.) Nice presentation with LaTeX and graph.
• September 27th 2010, 10:09 PM
iamanoobatmath
Quote:

Originally Posted by undefined
Nice presentation with LaTeX and graph.

Wolframlpha is a life safer when the bloody textbook and the solution manual only gives answers to odd questions. (Headbang)

Nice name, btw. (Giggle)