Question

The first line segment follows y equals 3.5 x, restricted 1 less-than-or-equal-to x less-than 5. The first line segment is solid and ends with an open point on the ascending end. The second line segment follows y equals 2.25 x, restricted x greater-than-or-equal-to 5. The second line segment is dotted.


A store is having a sale on boxes of cereal. In the following piecewise function, the independent variable represents the number of boxes purchased. If fewer than five boxes are purchased, the cost per box is $3.50. If five or more boxes are purchased, the cost per box is only $2.25.

f(x)={3.50x if 1≤x<52.25x if x≥5


Does the graph accurately represent the situation? Why or why not?

(1 point)
Responses

No. The graph should be a single, continuous function.
No. The graph should be a single, continuous function.

No. It doesn’t pass the Vertical Line Test.
No. It doesn’t pass the Vertical Line Test.

No. All the endpoints should have closed circles.
No. All the endpoints should have closed circles.

Yes. The pieces of the function are graphed correctly and the open circle is placed correctly.

Answer 1

Yes. The pieces are graphed correctly: the $3.50x$ line stops just before x = 5 (open circle) and the $2.25x$ piece begins at x = 5 (included), so the graph matches the piecewise definition.