Learn basic function definitions and their graph shapes (eg: polynomial, rational, absolute value, step) and how to transform them (eg: reflections, stretching, contracting, shifting -- both vertically and horizontally).
f(x) = a*|x - h| + k
g(x) = a*floor(b*x - h) + k
Those two functions (absolute value and floor) could be used to define the piecewise function in your exercise.
The parameters a, b, h and k control the transformations.
That's a quick way, but the entire topic of transforming various functions to form specific piecewise functions requires weeks of instruction and practice.
If you don't have a graphing calculator, then you could experiment at the site below. They've put together an interactive graph where you can set the parameters a,h,k on the floor function, in order to observe how the (purple) graph changes. It's too bad they forgot parameter b, but you can click in the blue and green function definitions and try multiplying x by your own values of b.
www.desmos.com
g(x) = a*floor(b*x - h) + k
a = step height parameter
b = step length parameter
h = horizontal shift parameter
k = vertical shift parameter
The following thread contains an absolute value function transformed to fit a piecewise function. You may find it helpful, but, if not, at least it might generate some specific questions.
This was on a friend’s precalculus packet: What I initially thought to do was substitute the restriction’s number into the respective equation, but my final graphed piecewise didn’t match the key. For example, for the first equation, I substituted 1 like this: (-1)^3+1 and got the coordinate...
www.freemathhelp.com
I regret that your situation has apparently caused you to miss instruction, but without knowing whether you understand things like absolute value functions or any function transformations, I'm not sure what else to add. I'll wait for you to provide more context. Cheers
