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)
Responses

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

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

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

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

Answer 1

No. There should be open circles at the first point of two pieces.

Explanation: The second piece is defined for 3 < x ≤ 6, so at x = 3 the second-piece point must be open (the first piece has a closed point at (3, 0.5)). The third piece is defined for x > 6, so at x = 6 the third-piece point must be open (the second piece has a closed point at (6, 1.0)).