Piecewise-defined Function....2

[mathdad]

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

 

[MarkFL]

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:

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

Now, since we have by definition:

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

And:

\(\displaystyle 0=-0\)

We may simplify the given function by writing:

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

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 $(0,\infty)$.

View attachment 6653

 

[mathdad]

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

 

[MarkFL]

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

Yes. :D

 

[mathdad]

I use wolfram for all my graphs.