how do you get the equations of a piecewise function graph???

Question

hi, im having a mid-term, and my teacher says we're going to have to know how to get the piecewise EQUATIONS from a piecewise graph, as well as a piecewise GRAPH from a piecewise equation. I got the graph from the equation part, but how do you get the equation from the graph?

Answer 1

You just look at the graph from left to right and notice the places where it stops "behaving" the same way: i.e. it goes from a straight line to a curve, or another straight line with a different slope, or even a gap.

Then you look at the x-values where the "breaks" happen, and those x-values will divide your function into regions.

So for instance, the absolute value function is piecewise.

You can write it as:

f(x) = |x|

But since |x| = -x for x < 0 and x for x ≥0, the "break" happens at x = 0, and you could write instead:

f(x) = -x if -∞ < x < 0, x if 0 ≤ x < ∞