Use the image to answer the question.

Question

Three line segments are graphed on a coordinate plane. The x-axis ranges from 0 to 10 in increments of 0.5. The y-axis ranges from 0 to 6 in increments of 0.5.

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.

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. There should be an open circle on the first point of two parts of the function.

Answer 1

The correct response is:

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

This is because the piecewise function specifies that the dosage for certain age intervals is not inclusive at the endpoints for some of the segments. Specifically, the first segment ends at \(x = 3\) with a dosage of \(1.0\), but it does not actually include the dosage at \(x = 3\) (the function is defined for \(1 \leq x \leq 3\)), which means there should be an open circle at that endpoint in the graph.