Question

graph the piecewise function f(x) = { x + 5 if x ≤ -2
2x + 3 if x > -2
will the graph have any endpoints? if yes, where?

Answer 1

Graph y = x + 5 for x ≤ −2 and y = 2x + 3 for x > −2.

At x = −2:
- The left piece (x + 5) includes x = −2, giving the closed point (−2, 3).
- The right piece (2x + 3) excludes x = −2; its value at −2 would be −1, so there is an open point (−2, −1).

So yes: there is a closed endpoint at (−2, 3) and an open endpoint (a hole) at (−2, −1). The two rays extend leftward and rightward respectively, producing a jump discontinuity at x = −2.