2.1E: Exercises

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Jun 4, 2023
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- 2.1: Relations and functions
- 2.2: Graphing on the Cartesian Coordinate Plane

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Practice Makes Perfect

Represent Relations as Mapping Diagrams and Tables

For each of the following relations, create a mapping diagram and table.

$R = \{(-17, 3), (4, 2), (2, 0), (6, -10), (7, 8)\}$
$R = \{(0, 3), (0, -5), (0, 7), (3, 22), (5, 16), (7, 3), (7, -11)\}$
$R = \{(-5, -1), (-4, 0), (-3, 1), (-2, 2)\}$
$R = \{(-3, 0), (-2, 3), (-2, 4), (1, -5)\}$

Answer

Mapping diagram	Table
$exercises_dr_map_1.JPG$	$\begin{array} {\|c\|c\|}\hline x & y \\\hline -17 & -10 \\ \hline 2 & 0 \\ \hline 4 & 2 \\ \hline 6 & 3 \\ \hline 7 & 8 \\ \hline \end{array}$

Mapping diagram	Table
$exercises_dr_map_2.JPG$	$\begin{array} {\|c\|c\|}\hline x & y \\\hline 0 & -5 \\ \hline 0 & 3\\ \hline 0 & 7 \\ \hline 3 & 22 \\ \hline 5 & 16 \\ \hline 7 & -11 \\ \hline 7 & 3 \\ \hline \end{array}$

Mapping diagram	Table
$exercises_dr_map_3.JPG$	$\begin{array} {\|c\|c\|}\hline x & y \\\hline -5 & -1 \\ \hline -4 & 0\\ \hline -3 & 1\\ \hline -2 & 2 \\ \hline \end{array}$

Mapping diagram	Table
$exercises_dr_map_4.JPG$	$\begin{array} {\|c\|c\|}\hline x & y \\\hline -3 & 0 \\ \hline -2 & 3\\ \hline -2 & 4\\ \hline 1 & 5 \\ \hline \end{array}$

Determine the domain of a relation

For each relation below, determine the domain.

$R = \{(-17, 3), (4, 2), (2, 0), (6, -10), (7, 8)\}$
$R = \{(0, 3), (0, -5), (0, 7), (3, 22), (5, 16), (7, 3), (7, -11)\}$
$R = \{(-5, -1), (-4, 0), (-3, 1), (-2, 2)\}$
$R = \{(-3, 0), (-2, 3), (-2, 4), (1, -5)\}$

Answer

$\{-17, 2, 4, 6, 7\}$
$\{0, 3, 5, 7\}$
$\{-5, -4, -3, -2\}$
$\{-3, -2, 1\}$

Determine the range of a relation

For each relation below, determine the range.

$R = \{(-17, 3), (4, 2), (2, 0), (6, -10), (7, 8)\}$
$R = \{(0, 3), (0, -5), (0, 7), (3, 22), (5, 16), (7, 3), (7, -11)\}$
$R = \{(-5, -1), (-4, 0), (-3, 1), (-2, 2)\}$
$R = \{(-3, 0), (-2, 3), (-2, 4), (1, -5)\}$

Answer

$\{-10, 0, 2, 3, 8\}$
$\{-11, -5, 3, 7, 16, 22\}$
$\{-1, 0, 1, 2\}$
$\{-5, 0, 3, 4\}$

Determine the domain and range of a relation

For each relation below, find the domain and range.

$R = \{(-13, 7), (2, 4), (0, 0), (10, 6), (8, 7)\}$
$R = \{(1, 1), (-1, -4), (-1, 6), (2, 21), (4, 15), (6, 2), (6, -10)\}$
$R = \{(-4, 0), (-3, -1), (-4, 0), (-1, 1)\}$
$R = \{(-2, 1), (-1, 4), (-3, 5), (0, -5)\}$

Answer

Domain: $\{-13, 0, 2, 8, 10\}$ ; Range: $\{0, 4, 6, 7\}$
Domain: $\{-1, 1, 2, 4, 6\}$ ; Range: $\{-10, -4, 1, 2, 15, 21\}$
Domain: $\{-4, -3, -1\}$ ; Range: $\{-1, 0, 1\}$
Domain: $\{-3, -2, -1, 0\}$ ; Range: $\{-5, 1, 4, 5\}$

Determine the domain and range of a relation using a table

For each relation below, determine the domain and range.

$\begin{array} {|c|c|}\hline x & y \\ \hline -3 & -10 \\ \hline -2 & 3 \\ \hline 0 & -1 \\ \hline 1 & 4 \\ \hline 1 & 6 \\ \hline 5 & 10 \\ \hline 6 & 11 \\ \hline \end{array}$

$\begin{array} {|c|c|}\hline x & y \\ \hline -6 & 13 \\ \hline -5 & 31 \\ \hline -3 & -11 \\ \hline -2 & 2 \\ \hline -1 & 8 \\ \hline 0 & -6 \\ \hline 2 & -6 \\ \hline \end{array}$

$\begin{array} {|c|c|}\hline x & y \\ \hline -4 & 4 \\ \hline 2 & -2 \\ \hline 3 & -2 \\ \hline 3 & 3 \\ \hline 3 & -3 \\ \hline 10 & -10 \\ \hline 14 & -14 \\ \hline \end{array}$

Answer

Domain: $\{-3, -2, 0, 1, 5, 6\}$ ; Range: $\{-10, -1, 3, 4, 6, 10, 11\}$
Domain: $\{-6, -5, -3, -2, -1, 0, 2\}$ ; Range: $\{-11, -6, 2, 13, 31\}$
Domain: $\{-4, 2, 3, 10, 14\}$ ; Range: $\{-14, -10, -3, -2, 2, 3, 4\}$

Determine if a relation is a function

Determine if the following relations are functions:

$R = \{(-13, 7), (2, 4), (0, 0), (10, 6), (8, 7)\}$
$R = \{(1, 1), (-1, -4), (-1, 6), (2, 21), (4, 15), (6, 2), (6, -10)\}$
$R = \{(-4, 0), (-3, -1), (-4, 1), (-1, 1)\}$
$R = \{(-2, 1), (-1, 4), (-3, 5), (0, -5)\}$
$R = \{(-17, 3), (4, 2), (2, 0), (6, -10), (7, 8)\}$
$R = \{(0, 3), (0, -5), (0, 7), (3, 22), (5, 16), (7, 3), (7, -11)\}$
$R = \{(-5, -1), (-4, 0), (-3, 1), (-2, 2)\}$
$R = \{(-3, 0), (-2, 3), (-2, 4), (1, -5)\}$

Answer

Function
Not a function
Not a function
Function
Function
Not a function
Function
Not a function

Evaluate a function represented with ordered pairs

For each function below, evaluate the following: $f(-1), f(0), f(3)$

$f = \{(-1, 3), (0, 5), (3, 16)\}$
$f = \{(-4, 5), (-1, 2), (0, 5), (3, 5)\}$
$f = \{(-13, 7), (-1, -1), (2, 4), (0, 0), (3, 4) (10, 6), (8, 7)\}$
$f = \{(-5, -1), (-4, 0), (-3, 1), (-2, 2), (-1, 12), (0, -4), (3, -2)\}$
$f = \{(-3, 0), (-2, 3), (-1, 9), (0, 4), (1, -5), (3, -14), (9, 2)\}$

Answer

$f(-1) = 3; f(0) = 5; f(3) = 16$
$f(-1) = 2; f(0) = 5; f(3) = 5$
$f(-1) = -1; f(0) = 0, f(3) = 4$
$f(-1) = 12; f(0) = -4; f(3) = -2$
$f(-1) = 9; f(0) = 4; f(3) = -14$

Evaluate functions defined using an equation

For each function below, evaluate the following: $f(-3), f(0), f(5)$

$f(x) = 2x + 1$
$f(x) = x^2 + 1$
$f(x) = \sqrt{x + 4}$
$f(x) = |x| + 5$
$f(x) = -17$
$f(x) = 3x - 4$
$f(x) = 2x^2 - 2$
$f(x) = \sqrt{x + 4} + 9$
$f(x) = -2|x| + 3$
$f(x) = 3$

Answer

$f(-3) = -5; f(0) = 1, f(5) = 11$
$f(-3) = 10; f(0) = 1; f(5) = 26$
$f(-3) = 1; f(0) = 2; f(5) = 3$
$f(-3) = 8; f(0) = 5; f(5) = 10$
$f(-3) = -17; f(0) = -17; f(5) = -17$
$f(-3) = -13; f(0) = -4; f(5) = 11$
$f(-3) = 16; f(0) = -2; f(5) = 48$
$f(-3) = 10; f(0) = 11; f(5) = 12$
$f(-3) = -3; f(0) = 3; f(5) = -7$
$f(-3) = 3; f(0) = 3; f(5) = 3$

Find the domain and range of a function defined using an equation

Find the domain and range for each of the functions below:

$f(x) = 2x + 1$
$f(x) = x^2 + 1$
$f(x) = \sqrt{x + 4}$
$f(x) = |x| + 5$
$f(x) = -17$
$f(x) = 3x - 4$
$f(x) = 2x^2 - 2$
$f(x) = \sqrt{x + 4} + 9$
$f(x) = -2|x| + 3$
$f(x) = 3$

Answer

Domain: $(-\infty, \infty)$ ; Range: $(-\infty, \infty)$
Domain: $(-\infty, \infty)$ ; Range: $(1, \infty)$
Domain: $x \geq -4$ ; Range: $y \geq 0$
Domain: $(-\infty, \infty)$ ; Range: $y \geq 5$
Domain: $(-\infty, \infty)$ ; Range: $y = -17$
Domain: $(-\infty, \infty)$ ; Range: $(-\infty, \infty)$
Domain: $(-\infty, \infty)$ ; Range: $(-2, \infty)$
Domain: $x \geq -4$ ; Range: $y \geq 9$
Domain: $(-\infty, \infty)$ ; Range: $y \leq 3$
Domain: $(-\infty, \infty)$ ; Range: $y = 3$

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Represent Relations as Mapping Diagrams and Tables

Determine the domain of a relation

Determine the range of a relation

Determine the domain and range of a relation

Determine the domain and range of a relation using a table

Determine if a relation is a function

Evaluate a function represented with ordered pairs

Evaluate functions defined using an equation

Find the domain and range of a function defined using an equation

Practice Makes Perfect

Represent Relations as Mapping Diagrams and Tables

Determine the domain of a relation

Determine the range of a relation

Determine the domain and range of a relation

Determine the domain and range of a relation using a table

Determine if a relation is a function

Evaluate a function represented with ordered pairs

Evaluate functions defined using an equation

Find the domain and range of a function defined using an equation

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