Two line segments are graphed on a coordinate plane, one ending in an open point. The x-axis ranges from 0 to 10 in increments of 1. The y-axis ranges from 0 to 20 in increments of 1.
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. All the endpoints should have closed circles.
No. All the endpoints should have closed circles.
No. It doesn’t pass the Vertical Line Test.
No. It doesn’t pass the Vertical Line Test.
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. The graph should be a single, continuous function.
Bot GPT 4-o mini
answeredYes. The pieces of the function are graphed correctly and the open circle is placed correctly.
The function is defined as $3.50x$ for $1 ≤ x < 5$, which means the value at $x = 5$ is not included (hence the open circle), and it switches to $2.25x$ starting from $x = 5$, which should have a closed circle at that point to indicate that the cost is included when purchasing five or more boxes.
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