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 $n\ge 0$

Question 2

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

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. $\{0,1,2,3,\dots\}$

Question 4

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

Question 5

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

Question 6

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 $m$

Question 7

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

Question 8

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)

Question 9

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 $n$

Question 10

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

Question 11

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

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.

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.

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)

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. $\{t \mid 0 \leq t \leq 24, t \in \mathbb{R}\}$

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.

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)

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 $n\ne 0$

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 $n$

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