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

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

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.

Answer 1

The correct response is:

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

The piecewise function is defined so that for \( 1 \leq x < 5 \), the cost is \( 3.50x \), which would be represented with a closed circle at \( x = 1 \) and an open circle at \( x = 5 \). For \( x \geq 5 \), the cost is \( 2.25x \), which correctly starts at \( x = 5 \) with a closed circle. Therefore, the graph accurately represents the situation described by the piecewise function.