Children’s cough syrup has dosage guidelines based on a child’s age. In the following piecewise function, x represents the child’s age in years and f(x) represents the dosage in fluid ounces.
f(x)=⎧⎩⎨⎪⎪0.5 if 1≤x≤31.0 if 3<x≤60.5x if x>6
Does the graph accurately represent the piecewise function? Why or why not?
A) No. The graph should be continuous, with all the pieces connected.
B) No. There should be an open circle on the first point of two parts of the function.
C) Yes, because all of the points at the ends of the pieces of the function should have closed circles.
D) Yes. The graph is correct because all three pieces of the function are present.
B) No. There should be an open circle on the first point of two parts of the function.
The piecewise function states that the dosage is 0.5 for ages between 1 and 3, and increases to 1.0 for ages between 3 and 6. According to the graph, the dosage abruptly changes from 0.5 to 1.0 at the age of 3 without an open circle at the age of 3 to indicate that the endpoint is not included. Therefore, the graph does not accurately represent the piecewise function.