Question

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?

(1 point)

No. There should be an open circle on the first point of two parts of the function.

No. The graph should be continuous with all the pieces connected.

Yes, because all of the points at the ends of the pieces of the function should have closed circles.

Yes. The graph is correct because all three pieces of the function are present.

Answer 1

No. There should be open circles at the left endpoints where the inequalities are strict.

The intervals are (1,3], (3,6], (6,∞). So the pieces that begin at x = 3 and x = 6 must start with open circles (while the previous pieces can have closed dots at those x-values).