Question

A dog groomer charges her clients by the weight of the dog. The following piecewise function represents the total charge, f(x) , for a dog weighing x pounds.What would be the last point graphed on the first piece of the function, f(x)=2.5x?

Answer 1

I don’t have the breakpoint for the piecewise function, so I can’t give a numeric point yet. In general, the last point of the first piece occurs at the x-value where the piece ends (call it x = a). Its coordinates are (a, 2.5a). Whether that endpoint is filled or open depends on the inequality in the piecewise rule (≤ gives a filled dot, < gives an open dot).

If you give the domain for the first piece (for example, 0 ≤ x ≤ 30), I’ll compute the exact last point (for 0 ≤ x ≤ 30 it would be (30, 75)).