Relating Domain to Context and Graphs - Algebra
Card 1 of 30
What domain is represented by a graph drawn only for $x\le -1$?
What domain is represented by a graph drawn only for $x\le -1$?
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$(-\infty,-1]$. Infinity is open, bracket includes $-1$.
$(-\infty,-1]$. Infinity is open, bracket includes $-1$.
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What is the domain of $f(x)=\frac{1}{x(x-5)}$ over the real numbers?
What is the domain of $f(x)=\frac{1}{x(x-5)}$ over the real numbers?
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All real $x$ except $x=0$ and $x=5$. Denominator $x(x-5)$ cannot equal zero.
All real $x$ except $x=0$ and $x=5$. Denominator $x(x-5)$ cannot equal zero.
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What is the domain of $f(x)=\frac{\sqrt{x+2}}{x-4}$ over the real numbers?
What is the domain of $f(x)=\frac{\sqrt{x+2}}{x-4}$ over the real numbers?
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$x\ge -2$ and $x\ne 4$. Need $x\ge -2$ for square root and $x\ne 4$ for denominator.
$x\ge -2$ and $x\ne 4$. Need $x\ge -2$ for square root and $x\ne 4$ for denominator.
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What is an appropriate domain for $V(t)$ = volume of water after $t$ minutes of filling?
What is an appropriate domain for $V(t)$ = volume of water after $t$ minutes of filling?
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All real $t\ge 0$ (often until the container is full). Time starts at $0$ and continues until full.
All real $t\ge 0$ (often until the container is full). Time starts at $0$ and continues until full.
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Which domain best matches $m(a)$ = monthly payment depending on APR $a$ (in decimal)?
Which domain best matches $m(a)$ = monthly payment depending on APR $a$ (in decimal)?
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All real $a>0$ (in the realistic range for APR). APR must be positive for realistic loan calculations.
All real $a>0$ (in the realistic range for APR). APR must be positive for realistic loan calculations.
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Which domain is appropriate for $T(n)$ = total points after $n$ games played?
Which domain is appropriate for $T(n)$ = total points after $n$ games played?
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Nonnegative integers $n=0,1,2,\dots$. Can have played zero or any whole number of games.
Nonnegative integers $n=0,1,2,\dots$. Can have played zero or any whole number of games.
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What is the domain of $f(x)=|x-7|$ over the real numbers?
What is the domain of $f(x)=|x-7|$ over the real numbers?
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All real numbers. Absolute value is defined for all real numbers.
All real numbers. Absolute value is defined for all real numbers.
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What is the domain of $f(x)=\sqrt{(x-4)^2}$ over the real numbers?
What is the domain of $f(x)=\sqrt{(x-4)^2}$ over the real numbers?
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All real numbers. $(x-4)^2$ is always non-negative, so square root exists.
All real numbers. $(x-4)^2$ is always non-negative, so square root exists.
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Identify the domain of $f(x)=\frac{2}{(x+1)^2}$ over the real numbers.
Identify the domain of $f(x)=\frac{2}{(x+1)^2}$ over the real numbers.
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All real $x$ except $x=-1$. Denominator $(x+1)^2$ cannot equal zero.
All real $x$ except $x=-1$. Denominator $(x+1)^2$ cannot equal zero.
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Which domain is appropriate for $c(n)$ = cost to ship $n$ boxes?
Which domain is appropriate for $c(n)$ = cost to ship $n$ boxes?
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Positive integers $n=1,2,3,\dots$. Must ship at least one box.
Positive integers $n=1,2,3,\dots$. Must ship at least one box.
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Which interval notation matches the domain $x<1$ or $x\ge 5$?
Which interval notation matches the domain $x<1$ or $x\ge 5$?
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$(-\infty,1)\cup[5,\infty)$. Union combines two separate intervals.
$(-\infty,1)\cup[5,\infty)$. Union combines two separate intervals.
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Which interval notation matches the domain $-6<x\le 2$?
Which interval notation matches the domain $-6<x\le 2$?
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$(-6,2]$. Parenthesis excludes $-6$, bracket includes $2$.
$(-6,2]$. Parenthesis excludes $-6$, bracket includes $2$.
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Which interval notation matches the domain $x\ge -4$?
Which interval notation matches the domain $x\ge -4$?
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$[-4,\infty)$. Bracket means $-4$ is included, infinity is always open.
$[-4,\infty)$. Bracket means $-4$ is included, infinity is always open.
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What is the domain of $f(x)=\frac{x^2-1}{x-1}$ when viewed as a rational expression?
What is the domain of $f(x)=\frac{x^2-1}{x-1}$ when viewed as a rational expression?
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All real $x$ except $x=1$. Denominator cannot be zero even though it simplifies to $x+1$.
All real $x$ except $x=1$. Denominator cannot be zero even though it simplifies to $x+1$.
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What is the domain of $f(x)=\frac{x}{x}$ when viewed as a rational expression?
What is the domain of $f(x)=\frac{x}{x}$ when viewed as a rational expression?
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All real $x$ except $x=0$. Cannot divide by zero even though $\frac{x}{x}=1$ when $x\ne 0$.
All real $x$ except $x=0$. Cannot divide by zero even though $\frac{x}{x}=1$ when $x\ne 0$.
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Which domain is appropriate for $b(t)$ = bank balance $t$ days after opening an account?
Which domain is appropriate for $b(t)$ = bank balance $t$ days after opening an account?
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All real $t\ge 0$ (often integers if measured by whole days). Time cannot be negative, may be continuous or discrete.
All real $t\ge 0$ (often integers if measured by whole days). Time cannot be negative, may be continuous or discrete.
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What is the domain of the quadratic function $f(x)=x^2-4x+1$ over the reals?
What is the domain of the quadratic function $f(x)=x^2-4x+1$ over the reals?
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All real numbers. Quadratic functions are defined for all real numbers.
All real numbers. Quadratic functions are defined for all real numbers.
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What domain should be used for $A(r)=\pi r^2$ when $r$ is a radius?
What domain should be used for $A(r)=\pi r^2$ when $r$ is a radius?
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All real $r\ge 0$. Radius must be non-negative in geometric contexts.
All real $r\ge 0$. Radius must be non-negative in geometric contexts.
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What domain should be used for $C(d)=3.50d$ if $d$ is distance traveled in miles?
What domain should be used for $C(d)=3.50d$ if $d$ is distance traveled in miles?
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All real $d\ge 0$. Distance cannot be negative in real-world contexts.
All real $d\ge 0$. Distance cannot be negative in real-world contexts.
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What domain should be used for $P(n)=12n$ if $n$ is the number of items purchased?
What domain should be used for $P(n)=12n$ if $n$ is the number of items purchased?
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Nonnegative integers $n=0,1,2,\dots$. Can purchase zero or any whole number of items.
Nonnegative integers $n=0,1,2,\dots$. Can purchase zero or any whole number of items.
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What domain should be used for $g(t)$ = height of a ball $t$ seconds after it is thrown?
What domain should be used for $g(t)$ = height of a ball $t$ seconds after it is thrown?
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All real $t\ge 0$ (often until the ball hits the ground). Time starts at $0$ and continues until impact.
All real $t\ge 0$ (often until the ball hits the ground). Time starts at $0$ and continues until impact.
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Which domain best matches a function $p(w)$ giving price for $w$ pounds of fruit?
Which domain best matches a function $p(w)$ giving price for $w$ pounds of fruit?
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All real $w\ge 0$. Weight must be non-negative for pricing.
All real $w\ge 0$. Weight must be non-negative for pricing.
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Which domain best matches a function $s(n)$ giving the $n$th term of a sequence?
Which domain best matches a function $s(n)$ giving the $n$th term of a sequence?
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Positive integers $n=1,2,3,\dots$. Sequence terms are indexed by positive integers.
Positive integers $n=1,2,3,\dots$. Sequence terms are indexed by positive integers.
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What does a closed dot at $x=4$ indicate about the domain endpoint?
What does a closed dot at $x=4$ indicate about the domain endpoint?
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The value $x=4$ is included in the domain. Closed dot means the endpoint is included.
The value $x=4$ is included in the domain. Closed dot means the endpoint is included.
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What does an open circle at $x=4$ indicate about the domain endpoint?
What does an open circle at $x=4$ indicate about the domain endpoint?
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The value $x=4$ is not included in the domain. Open circle means the endpoint is excluded.
The value $x=4$ is not included in the domain. Open circle means the endpoint is excluded.
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What domain is represented by a graph drawn only for $-2\le x<5$?
What domain is represented by a graph drawn only for $-2\le x<5$?
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$[-2,5)$. Bracket includes $-2$, parenthesis excludes $5$.
$[-2,5)$. Bracket includes $-2$, parenthesis excludes $5$.
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What domain is represented by a graph drawn only for $x>3$?
What domain is represented by a graph drawn only for $x>3$?
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$(3,\infty)$. Parenthesis excludes $3$, infinity is always open.
$(3,\infty)$. Parenthesis excludes $3$, infinity is always open.
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What is the domain of a function whose graph exists for all $x$ except a hole at $x=2$?
What is the domain of a function whose graph exists for all $x$ except a hole at $x=2$?
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All real $x$ except $x=2$. Hole means that specific $x$-value is excluded.
All real $x$ except $x=2$. Hole means that specific $x$-value is excluded.
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What is the domain of a function whose graph begins at $x=0$ with a closed dot and continues right?
What is the domain of a function whose graph begins at $x=0$ with a closed dot and continues right?
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$[0,\infty)$. Closed dot includes the starting point $x=0$.
$[0,\infty)$. Closed dot includes the starting point $x=0$.
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What is the domain of a function whose graph begins at $x=0$ with an open circle and continues right?
What is the domain of a function whose graph begins at $x=0$ with an open circle and continues right?
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$(0,\infty)$. Open circle excludes the starting point $x=0$.
$(0,\infty)$. Open circle excludes the starting point $x=0$.
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