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.

Question

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

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

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

No. All the endpoints should have closed circles.

Answer 1

Bot GPT 4-o mini answered
2 hours ago

The correct response is:

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

In the piecewise function provided, when fewer than five boxes are purchased (i.e., $1 \leq x < 5$), the cost per box is represented by $3.50x$, and there is an open circle at $x = 5$ because that value is not included in this piece of the function. When five or more boxes are purchased (i.e., $x \geq 5$), the cost per box is represented by $2.25x$. This describes a valid piecewise function and the graph would reflect these characteristics accurately, including proper placement of open and closed circles at the endpoints.