Which Description Is Represented by a Discrete Graph?

The answer

A description is represented by a discrete graph when the input can only take separate, countable values — usually whole numbers of individual items. The classic correct choice is a scenario like: "Kiley bought a platter for $19 and several matching bowls at $8 each." You can buy 1 bowl, 2 bowls, or 3 bowls, but never 2.5 bowls. Because the number of bowls jumps in whole steps, the graph is a set of unconnected dots, not a smooth line.

Why counting items makes it discrete

The test for discrete versus continuous is simple: ask whether the values between two points make sense.

• If the quantity is counted (bowls, tickets, students, cars), only whole numbers are meaningful. There is nothing between 3 bowls and 4 bowls, so the graph is discrete — a series of isolated points.
• If the quantity is measured (time, distance, weight, temperature, the amount of water in a tank), every value in between is possible, including fractions and decimals. That produces a continuous graph — an unbroken line or curve.

In the Kiley example, the total cost is 19 + 8b, where b is the number of bowls. Since b must be 0, 1, 2, 3, …, the plotted points are (0, 19), (1, 27), (2, 35), and so on — dots with gaps between them. Connecting them would falsely suggest you could spend, say, $31 on 1.5 bowls, which is impossible.

Why the other options are wrong

The distractors in this type of question usually describe measured, continuous quantities:

• "The distance a car travels over time" — time and distance can take any value, including fractions of a second and a meter, so the graph is a continuous line. Not discrete.
• "The amount of water draining from a tank" — volume decreases smoothly and continuously, taking every value in between. Not discrete.
• "A runner's height above the ground while jumping" — height is measured and changes continuously. Not discrete.

Each of these fails the counting test: you are measuring, not counting, so in-between values exist and the graph must be drawn as a connected curve. Only the scenario built on countable whole items produces the separated dots of a discrete graph.

The bigger picture

Money itself can be a subtle case. When money results from counting whole items at a fixed price — like bowls at $8 each — the totals land on separate values ($19, $27, $35), so it is discrete. But when money is treated as a smoothly varying amount (interest accruing continuously, or gallons of gas at $3.29 per gallon where you can buy any fraction of a gallon), it behaves continuously. The reliable rule to carry into any exam: counted things → discrete → dots; measured things → continuous → line. Match the description to whether its key quantity is counted or measured, and you will always pick the right graph.