Question

Use the image to answer the question.

Three line segments are graphed on a coordinate plane. The x axis ranges from 0 to 10 in increments of 1. The y axis ranges from 0 to 10 in increments of 1.
▶Click for Long Desc

Image Long DescriptionThe 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.

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. The graph is correct because all three pieces of the function are present.
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. 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, because all of the points at the ends of the pieces of the function should have closed circles.

Answer 1

No. The left endpoint at x = 1 should be open (the function is defined for 1 < x ≤ 3), but the graph shows a closed dot at (1, 0.5). Thus the graph does not match the piecewise definition.