How exactly do I graph piecewise functions?

Question

I am an Algebra 2 student and I am studying piecewise functions.
How exactly do I graph some piecewise functions like:

$$f(x) = \begin{cases} -x-5 &: x \le -3\\ 4 &: -3 < x < 2\\ 3x-4 &: x \ge 2 \end{cases}$$

I always seem to confuse $x$ and $y$ variables.

Thank you!

Answer 1

The graph of $f$ is all points of the form $(x,f(x))$. At each $x$ value, you want to put a dot at the point $(x,y)$ with $y=f(x)$. Mentally break the $x$-axis into sections (in this case $x\leq 3$, $-3<x<2$ and $x\geq 2$, and use what you know how to do on each of those pieces.