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First graph and then find the intervals of increasing and decreasing for piecewise function

First graph and then find the intervals of increasing and decreasing for piecewise-example-1
User Heloisasim
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1 Answer

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In order to graph this function, let's identify the type of graph of each part, and then calculate two or more points from each part:


\begin{gathered} x+2\to\text{ linear} \\ x=-2\colon \\ f(-2)=-2+2=0 \\ x=-3\colon \\ f(-3)=3+2=-1 \\ \\ x^2\to quadratic \\ x=-1\colon \\ f(-1)=(-1)^2=1 \\ x=0\colon \\ f(0)=0^2=0 \\ x=1\colon \\ f(1)=1^2=1 \\ \\ 1\to\text{constant} \\ x=2\colon \\ y=1 \\ x=3\colon \\ y=1 \end{gathered}

Graphing all these points and the corresponding lines or curves, we have:

Looking at the graph, we can see that the function is increasing for the interval:


(-\text{inf,}-1)\cup(0,1)

And the function is decreasing for the interval:


(-1,0)

First graph and then find the intervals of increasing and decreasing for piecewise-example-1
User JHowIX
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