Question

which description is represented by a discrete graph?
kiley bought a platter for $19 and several matching bowls that were $8 each. what is the total cost before tax?
the temperature at 9 a.m. was 83° f and is heating up at an average rate of 6°f per hour. what is the temperature x hours later?
juan ate an egg with 78 calories and some cereal with 110 calories per serving for breakfast. what is the total amount of calories he consumed?
a bottle contained 2,000 ml of liquid and is being poured out at an average rate of 300 ml per second. how much liquid is left in the bottle after x seconds?

Explanation:

Step1: Recall discrete vs continuous

Discrete graphs represent data with distinct, separate points (values that are countable, like number of items). Continuous graphs have connected points (values that can be any real number, like time, temperature, volume over time).

Step2: Analyze each option

• Option 1 (Kiley's bowls): Number of bowls is a non - negative integer (countable). Total cost \( C = 19+8n \), where \( n \) is number of bowls (discrete, \( n = 0,1,2,... \)).
• Option 2 (Temperature): \( x \) (hours) can be any real number (e.g., 1.5 hours), so temperature \( T=83 + 6x \) is continuous.
• Option 3 (Juan's calories): Number of cereal servings is a non - negative integer? Wait, no—wait, actually, if we consider "some cereal" as a serving, but the problem is similar to the first? Wait, no, the key is: in the first option, number of bowls is discrete (you can't buy a fraction of a bowl). In Juan's case, "some cereal"—but the first option has "several matching bowls" (discrete count). Wait, no, let's re - check. The first option: number of bowls \( n\in\{0,1,2,...\} \), so the graph of total cost vs number of bowls is discrete (points at \( n = 0,1,2,... \)). The third option: if we consider number of servings, but the problem says "some cereal"—but maybe the first is more clearly discrete. Wait, no, let's check again.

Wait, the first option: Kiley buys a platter (1 item) and several bowls (number of bowls is a whole number, discrete). So the total cost is a function of a discrete variable (number of bowls). The other options: temperature (x is continuous), liquid left (x seconds is continuous, can be a fraction), and Juan's calories—if we consider number of servings, but the problem says "some cereal"—but the first option is about a countable number of items (bowls). So the first option is discrete.

Wait, let's re - evaluate:

• Option 1: Let \( n \) be the number of bowls. \( n = 0,1,2,... \). Total cost \( C=19 + 8n \). The graph of \( C \) vs \( n \) has points at \( n = 0,1,2,... \), so it's discrete.

• Option 2: \( x \) (hours) can be any real number (e.g., 0.5, 2.3), so \( T = 83+6x \) is a continuous function (graph is a line).

• Option 3: Let \( s \) be the number of cereal servings. \( s = 0,1,2,... \). Total calories \( C = 78+110s \). But is this different from option 1? Wait, the problem is in the wording: "several matching bowls" vs "some cereal". But maybe the first option is the answer. Wait, no, maybe I made a mistake. Wait, the key is: in the first option, the independent variable (number of bowls) is discrete (countable, whole numbers). In the other options, the independent variable (x hours, x seconds, number of servings) — but in the case of liquid pouring, x seconds is continuous (you can have 0.5 seconds). In Juan's case, if we consider servings, it's discrete, but the first option is more clearly about a physical object (bowl) that is counted discretely.

Wait, the correct answer is the first option: "Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax?"

Answer:

Kiley bought a platter for $19 and several matching bowls that were $8 each. What is the total cost before tax?