Algebra Quiz: Relating Domain To Context And Graphs

What this quiz covers

This quiz focuses on Relating Domain To Context And Graphs, giving you a quick way to practice the rules, question types, and explanations that matter most for Algebra.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. All integers $n$ such that $0\le n\le 200$ (correct answer)
2. All real numbers $n$
3. All real numbers $n$ such that $0\le n\le 200$
4. All integers $n$ such that $n\ge 0$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of engines being assembled, we can't have n = -5 (negative engines) or n = 2.7 (partial engines), so the appropriate domain is positive integers {1, 2, 3, ...}, even though mathematically the formula might work for any number. In this scenario, n is the number of tickets sold in a theater with 200 seats, so n must be whole numbers from 0 (no tickets sold) to 200 (all seats filled), as you can't sell a fraction of a ticket or more than available seats. Choice C correctly identifies the domain as all integers n such that 0 ≤ n ≤ 200 because it accounts for the countable nature of tickets and the capacity limit. Choice A might seem appealing but allows non-integer values like n=1.5, which doesn't make sense for selling tickets. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 2

1. $[-1,4)$ (correct answer)
2. $(-1,4]$
3. $[-1,4]$
4. $( -\infty,\infty)$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). Reading domain from a graph: look at which x-values have corresponding points on the graph. If the graph extends from x = 0 to x = 5 with a continuous curve, the domain is [0, 5]. If it shows separate dots at x = 0, 1, 2, 3, 4, 5, the domain is {0, 1, 2, 3, 4, 5}—the graph itself tells you the domain! Here, the solid line segment starts at a closed point at x = -1 (included) and ends at an open point at x = 4 (excluded), so the domain covers all x from -1 to just before 4. Choice A correctly identifies the domain as [-1,4) because it matches the inclusion of -1 and exclusion of 4 as shown. Choice C includes 4, but the open point means it's not part of the graph. Graph clue: if you see a solid curve or line, the domain is an interval (continuous). If you see separated dots, the domain is a list of specific values (discrete). The visual representation directly shows whether the function is defined everywhere in an interval or just at certain points!

Question 3

1. All real numbers except $0$
2. $\{n\mid n\text{ is an integer and }n\ge 1\}$ (correct answer)
3. $[1,\infty)$ (all real numbers $n\ge 1$)
4. $\{0,1,2,3,\dots\}$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of engines being assembled, we can't have n = -5 (negative engines) or n = 2.7 (partial engines), so the appropriate domain is positive integers {1, 2, 3, ...}, even though mathematically the formula might work for any number. For the bakery packaging time P(n) = 60/n, n is the number of workers, which must be positive integers since you can't have zero, negative, or fractional workers, and the formula divides by n. Choice B correctly identifies the domain as {n | n is an integer and n ≥ 1} because it fits the real-life constraint of whole, positive numbers of people. Choice C allows fractions like 1.5 workers, which doesn't make practical sense here. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 4

1. All real numbers from 0 to 200: $[0,200]$
2. All integers from 0 to 200: $\{0,1,2,\dots,200\}$ (correct answer)
3. All positive real numbers: $(0,\infty)$
4. All integers

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of attendees in a 200-seat theater, we can't have n = -5 (negative attendees) or n = 150.5 (partial people), so the appropriate domain is integers from 0 to 200, even though mathematically the formula might work for any number. The theater context gives us two key constraints: attendees must be whole people (integers) and the theater has a maximum capacity of 200 seats. Choice B correctly identifies the domain as all integers from 0 to 200: {0, 1, 2, ..., 200} because you count people in whole numbers and the theater can have anywhere from 0 (empty) to 200 (full) attendees. Choice A [0, 200] would incorrectly allow fractional attendees like 125.7 people, which is impossible in real life. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 5

1. All real numbers $n\ge 0$
2. All integers
3. Non-negative integers $\{0,1,2,3,\dots\}$ (correct answer)
4. All real numbers

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of text messages sent, we can't have n = -10 (negative messages) or n = 5.5 (partial messages), so the appropriate domain is non-negative integers {0, 1, 2, 3, ...}, even though mathematically the formula might work for any number. Text messages are discrete items that are counted in whole numbers, and it's possible to send 0 messages in a month (just paying the base fee). Choice C correctly identifies the domain as non-negative integers {0, 1, 2, 3, ...} because messages are counted in whole units starting from zero. Choice A (all real numbers n ≥ 0) would incorrectly allow fractional messages like 15.7 messages, which isn't possible when counting actual text messages sent. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 6

1. (1) discrete points; (2) continuous line
2. (1) continuous line; (2) discrete points (correct answer)
3. (1) discrete points; (2) discrete points
4. (1) continuous line; (2) continuous line

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). When graphing functions, the domain determines whether we use a continuous line or curve (for measurable quantities like time, distance, or temperature) or discrete points (for countable quantities like number of people, items sold, or days). If you're counting things that come in whole units, use dots; if you're measuring continuous quantities, use a connected line or curve! For the cyclist, distance over time is continuous because time and distance can take any value, so a line; for stickers, n packs are countable wholes, so points. Choice B correctly pairs (1) continuous line for the cyclist and (2) discrete points for stickers, matching the nature of each variable. Choice A swaps them, but distance isn't discrete while stickers aren't continuous. For discrete vs continuous graphing: if the context involves counting distinct objects (tickets sold, students in class, days of the week), use separate dots because you can't have fractional amounts. If it involves measuring (time passing, distance traveled, temperature), use a connected line because the quantity can take any value in between. Think: 'Can there be in-between values?' If no, discrete. If yes, continuous!

Question 7

1. All integers $m$ such that $m\ge 0$ (correct answer)
2. All integers $m$ such that $m\ge 1$
3. All real numbers $m$ such that $m\ge 0$
4. All real numbers $m$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of engines being assembled, we can't have n = -5 (negative engines) or n = 2.7 (partial engines), so the appropriate domain is positive integers {1, 2, 3, ...}, even though mathematically the formula might work for any number. For the streaming service, m represents whole months since signing up, starting from 0 (initial sign-up with no months passed) and increasing as integers with no upper limit specified. Choice D correctly identifies the domain as all integers m such that m ≥ 0 because months are counted in whole units and can't be negative. Choice C allows real numbers, but you can't have a fraction of a month in this billing context. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 8

1. All real numbers $m$
2. All real numbers $m\ge 0$ (correct answer)
3. All integers $m\ge 0$
4. All real numbers $m\le 0$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). When graphing functions, the domain determines whether we use a continuous line or curve (for measurable quantities like time, distance, or temperature) or discrete points (for countable quantities like number of people, items sold, or days). If you're counting things that come in whole units, use dots; if you're measuring continuous quantities, use a connected line or curve! In this ride-share scenario, miles can be measured continuously (you can travel 2.5 miles, 3.14 miles, etc.), and you can't travel negative miles, so m must be non-negative. Choice B correctly identifies the domain as all real numbers m ≥ 0 because distance is continuous and non-negative. Choice C is incorrect because it restricts miles to integers only (0, 1, 2, 3 miles), missing fractional distances like 1.7 miles that are perfectly valid for a car trip. For discrete vs continuous graphing: if the context involves counting distinct objects (tickets sold, students in class, days of the week), use separate dots because you can't have fractional amounts. If it involves measuring (time passing, distance traveled, temperature), use a connected line because the quantity can take any value in between. Think: 'Can there be in-between values?' If no, discrete. If yes, continuous!

Question 9

1. $\{n\mid 0\le n\le 120,\ n\text{ is an integer}\}$ (correct answer)
2. $\{n\mid n\ge 0\}$ (all real numbers $n\ge 0$)
3. All real numbers
4. $[0,120]$ (all real numbers from 0 to 120)

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if $n$ represents the number of engines being assembled, we can't have $n = -5$ (negative engines) or $n = 2.7$ (partial engines), so the appropriate domain is positive integers $\{1, 2, 3, \dots\}$, even though mathematically the formula might work for any number. In this smoothie shop scenario, $n$ represents the number of smoothies made in a day, which must be whole numbers because you can't make a fraction of a smoothie, and it ranges from 0 (no smoothies) to 120 (maximum capacity), including 0 since the fixed cost applies even without making any. Choice B correctly identifies the domain as $\{n \mid 0 \le n \le 120, n \text{ is an integer}\}$ because it accounts for the contextual constraints of non-negative integers up to the shop's limit. Choice A is close but fails gently because it allows fractional values like 2.5 smoothies, which don't make sense in reality. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 10

1. Continuous line, because $n$ can be any real number
2. Separate points, because $n$ must be a whole number of shirts (correct answer)
3. Continuous line, because cost changes smoothly
4. Separate points, because $C(n)$ can be negative for some $n$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). When graphing functions, the domain determines whether we use a continuous line or curve (for measurable quantities like time, distance, or temperature) or discrete points (for countable quantities like number of people, items sold, or days). If you're counting things that come in whole units, use dots; if you're measuring continuous quantities, use a connected line or curve! In this case, n represents the number of T-shirts, which must be whole numbers, so the graph should show separate points at integer values rather than a continuous line. Choice B correctly identifies that it should be separate points because n must be a whole number of shirts. Choice A suggests a continuous line, but that would imply fractional shirts, which isn't realistic for ordering. For discrete vs continuous graphing: if the context involves counting distinct objects (tickets sold, students in class, days of the week), use separate dots because you can't have fractional amounts. If it involves measuring (time passing, distance traveled, temperature), use a connected line because the quantity can take any value in between. Think: 'Can there be in-between values?' If no, discrete. If yes, continuous!

Question 11

1. $\{0,1,2,3\}$
2. $(0,3)$
3. $[0,3]$ (correct answer)
4. All real numbers

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). When graphing functions, the domain determines whether we use a continuous line or curve (for measurable quantities like time, distance, or temperature) or discrete points (for countable quantities like number of people, items sold, or days). If you're counting things that come in whole units, use dots; if you're measuring continuous quantities, use a connected line or curve! In this ball-throwing situation, t represents time in seconds, which is a continuous quantity from the launch at t=0 until it hits the ground at t=3, including both endpoints as the height is defined there. Choice A correctly identifies the domain as [0,3] because time flows continuously without gaps in this physical context. Choice B doesn't quite fit because it treats time as discrete integers, but time isn't limited to whole seconds here. For discrete vs continuous graphing: if the context involves counting distinct objects (tickets sold, students in class, days of the week), use separate dots because you can't have fractional amounts. If it involves measuring (time passing, distance traveled, temperature), use a connected line because the quantity can take any value in between. Think: 'Can there be in-between values?' If no, discrete. If yes, continuous!

Question 12

1. $\{s \mid 0.5 \leq s \leq 12, s \in \mathbb{R}\}$ because side length can theoretically take any real value within the material constraints.
2. $\{0.5, 0.6, 0.7, 0.8, ..., 11.9, 12.0\}$ because the measurement tools limit precision to tenths of an inch within the material range. (correct answer)
3. $\{s \mid 0.5 \leq s \leq 12, s \in \mathbb{Q}\}$ because measurements are rational numbers, even though tools have limited precision.
4. $\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$ because geometric constructions in classroom settings typically use whole number measurements.

Explanation: The measurement tools that read to the nearest 0.1 inch create a practical constraint on the domain. Students can only measure and verify side lengths to this precision, so the meaningful domain consists of discrete values in tenths of inches. Choice A ignores the measurement limitation. Choice C incorrectly suggests all rational numbers are measurable. Choice D is too restrictive, ignoring both the lower bound (0.5) and the measurement precision (0.1 rather than 1).

Question 13

1. $t \geq 0$ since time cannot be negative in this context, and exponential growth models are valid for all non-negative real numbers.
2. $0 \leq t \leq 48$ since the culture exists from the initial observation until it dies, and fractional hours are meaningful in biological processes. (correct answer)
3. $\{0, 1, 2, 3, ..., 48\}$ since population counts are typically measured at discrete hourly intervals in laboratory settings.
4. $1 \leq t \leq 48$ since $t = 0$ represents the time before observation began, so it should be excluded from the meaningful domain.

Explanation: The bacteria culture exists from the initial observation time ($t = 0$) until it dies at $t = 48$ hours. Biological processes occur continuously, so fractional hours are meaningful. Choice A ignores the biological constraint that the culture dies. Choice C unnecessarily restricts to integers when continuous time makes biological sense. Choice D incorrectly excludes $t = 0$, which represents the valid initial observation time.

Question 14

1. $\{2, 3, 4, 5, 6, 7, 8\}$ since manufacturing typically works with standard integer millimeter sizes for ball bearings.
2. $\{r \mid 2 < r < 8, r \in \mathbb{R}\}$ since the exact boundary values are difficult to achieve in manufacturing processes.
3. $\{r \mid 2 \leq r \leq 8, r \in \mathbb{Q}\}$ since manufacturing equipment has finite precision, limiting measurements to rational numbers only.
4. $\{r \mid 2 \leq r \leq 8, r \in \mathbb{R}\}$ since radius measurements can take any real value within the specified range. (correct answer)

Explanation: When you encounter questions about function domains in real-world contexts, you need to consider both the mathematical constraints and the practical limitations of the situation. The domain represents all possible input values that make sense for the function. For this sphere volume function, the mathematical constraint is clear: the radius must be between 2 mm and 8 mm inclusive, as stated in the problem. The key insight is determining what types of numbers can represent radius measurements in manufacturing. Answer D is correct because radius measurements in manufacturing can theoretically take any real value within the specified range $\{r \mid 2 \leq r \leq 8, r \in \mathbb{R}\}$. While manufacturing equipment has limited precision, the domain describes all mathematically possible values, not just the ones we can practically measure. A radius could be exactly $\pi$ mm or $\sqrt{7}$ mm, even if our equipment can only approximate these values. Answer A incorrectly assumes manufacturing only uses integer values. Ball bearings are made in many fractional sizes. Answer B wrongly excludes the boundary values (2 mm and 8 mm) even though the problem states these are acceptable. Answer C limits the domain to rational numbers only, but there's no mathematical or practical reason why an irrational radius value couldn't exist. Study tip: When determining domains for real-world functions, distinguish between the mathematical domain (all theoretically possible values) and measurement limitations. Unless explicitly told otherwise, assume real numbers are possible within the given constraints.

Question 15

1. $\{t \mid 0 \leq t \leq 14, t \in \mathbb{R}\}$ (correct answer)
2. $\{t \mid 1 \leq t \leq 14, t \in \mathbb{Z}^+\}$
3. $\{t \mid 0 < t \leq 14, t \in \mathbb{R}\}$
4. $\{t \mid 0 \leq t \leq 24, t \in \mathbb{R}\}$

Explanation: The venue is available from 9 AM to 11 PM, which is 14 hours total. Since you can rent for any fraction of an hour (including 0 hours theoretically), the domain should include all real numbers from 0 to 14 hours, inclusive. Choice B incorrectly restricts to positive integers only. Choice C excludes 0 hours rental. Choice D uses 24 hours, which exceeds the venue's availability window.

Question 16

1. The domain must exclude negative values since production quantity cannot be negative, and must exclude values where profit becomes negative since companies cannot operate at a loss.
2. The domain must exclude negative values since production quantity cannot be negative, but should include all positive real numbers since any production level is theoretically possible.
3. The domain must exclude negative values since production quantity cannot be negative, and should be further restricted to practical production levels based on company capacity and market demand. (correct answer)
4. The domain should include all real numbers since the mathematical function is defined everywhere and business contexts should not restrict mathematical domains.

Explanation: In business contexts, production quantity $n$ cannot be negative, ruling out choice D. However, choice A incorrectly suggests excluding values where profit is negative - companies can operate temporarily at a loss. Choice B ignores practical constraints like production capacity. Choice C correctly identifies that the domain should exclude negative values and be further restricted by real-world business limitations like factory capacity and market size.

Question 17

1. $[0, \infty)$ because time cannot be negative, but the projectile could theoretically continue moving indefinitely after being launched.
2. $[0, 2]$ because the projectile reaches its maximum height at the vertex of the parabola at $t = 2$ seconds.
3. $(-\infty, \infty)$ because the mathematical function is defined for all real numbers and represents a continuous motion.
4. $[0, 4]$ because the projectile starts at $t = 0$ and returns to ground level when the height function equals zero again. (correct answer)

Explanation: When dealing with quadratic functions that model real-world situations like projectile motion, you need to determine the domain based on the physical constraints, not just the mathematical function. The key is finding when the situation begins and ends in reality. To find the appropriate domain for $h(t) = -16t^2 + 64t$, you need to determine when the projectile is actually in motion. Since it's launched from ground level, it starts at $t = 0$. To find when it returns to the ground, set the height equal to zero: $-16t^2 + 64t = 0$. Factoring gives $-16t(t - 4) = 0$, so $t = 0$ or $t = 4$. The projectile hits the ground again at $t = 4$ seconds, making the domain $[0, 4]$. Choice A is wrong because while time can't be negative, the projectile doesn't continue indefinitely—it hits the ground at $t = 4$ seconds and stops moving upward. Choice B misunderstands what determines the domain; the vertex tells you the maximum height occurs at $t = 2$, but the projectile continues moving until $t = 4$. Choice C ignores the physical reality—mathematically the function exists for all real numbers, but physically the projectile motion only makes sense from launch until it hits the ground. Remember: for real-world quadratic models, always find where the function equals zero to determine when the situation ends. The domain represents the time interval during which the physical situation actually occurs, not just where the math function is defined.

Question 18

1. All real numbers $n>0$
2. All integers $n$ such that $n\ge 2$
3. All integers $n$ such that $n\ge 1$ (correct answer)
4. All real numbers $n\ne 0$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of engines being assembled, we can't have n = -5 (negative engines) or n = 2.7 (partial engines), so the appropriate domain is positive integers {1, 2, 3, ...}, even though mathematically the formula might work for any number. Here, n is the number of friends splitting the cost, so it must be positive integers starting from 1, as 0 friends would cause division by zero and doesn't make sense for sharing. Choice C correctly identifies the domain as all integers n such that n ≥ 1 because friends are whole people and at least one is needed. Choice A allows real numbers greater than 0, but you can't have a fraction of a friend in this scenario. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 19

1. All real numbers $n$ such that $0\le n\le 120$
2. All integers $n$ such that $0\le n\le 120$ (correct answer)
3. All integers $n$ such that $1\le n\le 120$
4. All real numbers $n$

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of engines being assembled, we can't have n = -5 (negative engines) or n = 2.7 (partial engines), so the appropriate domain is positive integers {1, 2, 3, ...}, even though mathematically the formula might work for any number. For the bakery, n is the number of cupcakes, which must be whole numbers from 0 (no cupcakes made, just fixed costs) to 120 (maximum batch size), as partial cupcakes don't make sense in this context. Choice B correctly identifies the domain as all integers n such that 0 ≤ n ≤ 120 because it reflects the countable items and the production limit. Choice A allows real numbers like n=3.5, which isn't practical for baking whole cupcakes. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!

Question 20

1. $\{m\mid m\ge 0,\ m\text{ is an integer}\}$ (correct answer)
2. $\{m\mid m\text{ is an integer}\}$ (all integers)
3. $[0,\infty)$ (all real numbers $m\ge 0$)
4. All real numbers

Explanation: This question tests your understanding of how the domain of a function relates to both the context (what makes sense in real life) and the graph (how the function is represented visually). The domain is the set of all possible input values, and in real-world contexts, we need to think about what values actually make sense: if n represents the number of engines being assembled, we can't have n = -5 (negative engines) or n = 2.7 (partial engines), so the appropriate domain is positive integers {1, 2, 3, ...}, even though mathematically the formula might work for any number. In this phone plan, m is the number of months since activation, which starts at 0 and increases in whole numbers because months are counted discretely, and negative months don't exist. Choice C correctly identifies the domain as {m | m ≥ 0, m is an integer} because it fits the contextual need for non-negative integers without an upper limit specified. Choice D allows fractional months like 1.5, which might not make sense for billing cycles in this model. When determining domain from context, ask yourself: (1) What does the variable represent? (2) Can it be negative? (usually not for quantities, time, etc.) (3) Are there upper limits? (capacity, time limits) (4) Must it be whole numbers? (counting people/items) or can it be any number? (measuring distance/time). Answer these questions and the domain becomes clear!