MHB Piecewise-defined Function....2

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To graph the piecewise-defined function y(x) = |x| for x ≤ 0 and y(x) = x^3 for x > 0, first simplify it to y(x) = -x for x ≤ 0 and y(x) = x^3 for x > 0. Plot the line y = -x on the interval (-∞, 0] and the cubic function y = x^3 on the interval (0, ∞). The graph is created by drawing each piece separately on the same xy-plane. Using graphing tools like Wolfram can facilitate this process. Understanding how to graph piecewise functions accurately is essential for visualizing their behavior.
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What is the easiest way to graph a piecewise-defined function by hand?

y = | x | if x is < or = 0...this is the upper piece

y = x^3 if x > 0...this is the bottom piece
 
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RTCNTC said:
What is the easiest way to graph a piecewise-defined function by hand?

y = | x | if x is < or = 0...this is the upper piece

y = x^3 if x > 0...this is the bottom piece

We are given:

$$y(x)=\begin{cases}|x|, & x\le0 \\[3pt] x^3, & 0<x \\ \end{cases}$$

Now, since we have by definition:

$$|x|=\begin{cases}-x, & x<0 \\[3pt] x, & 0\le x \\ \end{cases}$$

And:

$$0=-0$$

We may simplify the given function by writing:

$$y(x)=\begin{cases}-x, & x\le0 \\[3pt] x^3, & 0<x \\ \end{cases}$$

And so, to plot this function by hand, we would draw the line $y=-x$ on the interval $(-\infty,0]$ and the cubic $y=x^3$ on the interval $(0,\infty)$.

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Are you saying we graph one piece at a time on the same xy-plane?
 
RTCNTC said:
Are you saying we graph one piece at a time on the same xy-plane?

Yes. :D
 
I use wolfram for all my graphs.
 
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