Question

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v Click for Long Desc
The first line segment follows y equals 0 point 5, from left parenthesis 1 comma space 0 point 5 right parenthesis to left parenthesis 3 comma space 0 point 5 right parenthesis with closed circles at both ends.
The second line segment follows y equals 1 from left parenthesis 3 comma space 1 right parenthesis to left parenthesis 6 comma space 1 right parenthesis with an open circle on one end and a closed circle on
the other. The third line segment follows y equals 0 point 5 x, from left parenthesis 6 comma space 3 right parenthesis with an open circle and an arrow at the right end.

Image Long Description

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.

0.5if1<x<3
f(x)=1.0if3<x ≤ 6
0.5x if x > 6

Does the graph accurately represent the piecewise function? Why or why not?

(1 point)

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

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

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.

Answer 1

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

Reason: f is defined for 1 < x < 3 (so the endpoints at x = 1 and x = 3 must be open) and for 3 < x ≤ 6 (so x = 3 is also open there, x = 6 closed). The graph incorrectly shows closed circles at the ends of the first segment (and at x = 3), so it does not match the piecewise definition.