function and relation worksheet with answer key
Step 1: Tell the class a story involving a real-world, linear functional relationship. << Feel free to download and enjoy these free worksheets on functions and relations .Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Functions And Relations Worksheet | Teachers Pay Teachers Domain: \(\); range: \((, 3]\); function: yes, 21. If any vertical line intersects the graph more than once, then the graph does not represent a function. <>
This worksheet is practice for the students on how to find the domain and range of a relation, decide if something is a function or not, and to express a relation using a table, graph, and mapping diagram. 4. In addition, since we can find a vertical line that intersects the graph more than once, we conclude that the graph is not a function. D \R(BJIBxCKoo-J-}wwfvv5s9["%VA This notation is used as follows: \(\begin{array} { l } { f ( x )\:\: =\:\:\: | x | - 2 } \\ { \:\:\:\:\:\downarrow \quad\quad\quad \downarrow } \\ { f ( \color{Cerulean}{- 5}\color{Black}{ )} = | \color{Cerulean}{- 5}\color{Black}{ |} - 2 = 5 - 2 = 3 } \end{array}\). So helpful with my homework. This relations functions worksheet may act as a last-minute tool to revise the function and relation problems before your exams. /Pattern << Reflections Over Intersecting Lines as Rotations. >> These two number lines define a flat surface called a plane4, and each point on this plane is associated with an ordered pair5 of real numbers \((x, y)\). /AIS false Worksheet 4.1 Relations and Functions Write each of the following as a relation, state the domain and range, then determine if it is a function. Relations Expressed as Graphing. The first 3 questions ask students to take a relation (given as a set of ordered pairs) and represent the relation as a table, graph, and mapping diagram. This assignment is also included in my:Algebra 1 Google Forms (, Functions and Relations Worksheets (Bundle), Relations, Functions, Domain and Range | Task Cards, Holt Algebra 4.2 Relations and Functions Worksheet DOC & PDF, Relations and Functions Worksheet (linear/non linear #2), Relations and Functions Notes and Worksheets, Relations and Functions Unit (Algebra 1 Unit 3), Functions and Linear Equations Quiz & Worksheet, Identifying Functions | Function or Not a Function Practice Worksheet, BACK TO SCHOOL | ALGEBRA 1 FUNCTIONS Bundle, Evaluating and Identifying Functions Worksheet, Relations and Functions Introduction Worksheets Bundle (Five Worksheets), Relations and Functions 2 (input-output boxes), Relations and Functions - Algebra 1 Skills Practice Worksheet, Algebra 1 Skills Practice Worksheets Bundle, Identifying Functions - Quick Coloring Activity, Domain and Range of Relations and Functions Quiz for Google Form/Quiz, Relations and Functions Worksheet (linear/non linear #1), RELATIONS AND FUNCTIONS: - IDENTIFY THE DOMAIN AND RANGE COLORING ACTIVITY # 2, Marie's Math Resources and Coloring Activities, Graphing Quadratic Functions in Standard Form Worksheets, Identifying Functions Independent Practice, Functions & Relations, Domain & Range Notes, Functions Unit Bundle - Algebra 1 Curriculum, Functions & Relations, Domain & Range, Function Notation Quiz, Daily Lessons in COMPARING & SORTING Preschool Lesson Plans, Algebra 1 Google Forms Semester 1 Digital Homework and Assessment Bundle. 3. Simplify \(\frac { q ( x + h ) - q ( x ) } { h }\) given \(q ( x ) = a x\). If f (x) = 2x 3, then find [f (0) + (f)] / 2 and value of x when (a) f(x) = 0 (b) f(x)= x and f(x) = f(1-x). d224f870063a40e098457059835651f2, 055c0d457aa04cdf98c57925f2da174b 8. 12 graphs.Worksheet 2: Finding range given domainRiddle. . New: \($22,000\); \(4\) years old: \($14,800\). Explore math program Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. I suggest using this as a note guide during the lesson. xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ <>
9. \(g ( - 3 ) = - 1 , g ( 0 ) = 1 , g ( 9 x + 6 ) = 6 x + 5\), 9. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>>
12The set consisting of all of the second components of a relation. D 25. 0000001962 00000 n
3. This system is often called the Cartesian coordinate system8, named after the French mathematician Ren Descartes (15961650). 2. Relations and Functions Worksheet Answer Key 1. /XObject << If any vertical line intersects the graph more than once, then the graph does not represent a function. 4.0,`
3p H.Hi@A> Value of [f(0) + f(1)] / 2 is -2, (a) x = 3/2 (b) x = 3 (c) x = , 13. Domain and Range (Algebra 1) Here we separate the domain (x-values), and the range (y-values), and depict the correspondence between the values with arrows. Two Items Included. Determine the domain and range and state whether the relation is a function or not. 0000001084 00000 n
4.2 Relations and Functions A function is a relation in . O*?f`gC/O+FFGGz)~wgbk?J9mdwi?cOO?w| x&mf
The intersection of the two axes is known as the origin6, which corresponds sto the point \((0, 0)\). Therefore, the domain consists of all \(x\)-values in the interval \([8,)\). 7. f(x) = x 8. h(x) = x + 7 9. g(x) = x - 2 10. g(x) = 3x 11. |E[v%D '_s;.C\{ b/01w$}1$>(EpyQx~_E6(
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@T1yDF,5M=]nOnD; Given the linear function defined by \(f(x)=2x-5\), simplify the following. A function is a relation in which each possible input value leads to exactly one output value. Research and discuss the life and contributions of Ren Descartes. 14. Range: Function: o 2 t 3 3 (3, 3) -2) Relation . Worksheet 4.1 relations and functions answer key. endobj Then they share a relationship and can be written as an ordered pair (x, y). 1. Given \(f ( x ) = \sqrt { 2 x + 4 }\), find \(f (2), f (0)\), and \(f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)\). Chapter 3: Introduction to Functions and Relations. >> Section 3.1. The minimum \(y\)-value represented on the graph is \(0\); thus, the range is \([0,)\). /CreationDate (D:20220708141653-04'00') Domain: \((, 0]\); range: \([1, )\); function: yes, 19. 15 33 17 15, 11 15 Relations Expressed as Graphing Write each of the following as a relation, state the domain and range, then determine if it is a function. Download Relations and Functions Worksheet PDFs These math worksheets should be practiced regularly and are free to download in PDF formats. %%EOF
\(f ( - 1 ) = 0 , f ( 0 ) = 1 , f \left( a ^ { 2 } \right) = a ^ { 6 } + 1\), 3. >> Write each of the following as a relation, state the domain and range, then determine if it is a function. {(3,2), (1, -1), (2, -4), (3, -9), (4, -16)} 4. Posted: 7/3/17 so 50% off through 7/6/17, Do your students need practice graphing real world quadratics? RELATIONS & FUNCTIONS Worksheet. Feel free to download and enjoy these free worksheets on functions and relations. Determine the domain and range of the following relation and state whether it is a function or not: \(\{(4, 3), (2, 6), (0, 3), (3, 5), (3, 7)\}\). 12. Included are 5 different task sheets. For instance, f(x) = root over x is an undefined function when the value of x is negative. Evaluate the inverse and also rule out whether the same is a function or not. Share a link to a page that you think others may find useful. <>
16The notation \(f (x) = y\), which reads \(f\) of \(x\) is equal to \(y\). Given a function, \(y\) and \(f (x)\) can be used interchangeably. Explain. [ -c R!z"^Ow,c 2The horizontal number line used as reference in a rectangular coordinate system. How to Determine Whether a Given Relation is a Function or Not? Special relations where every \(x\)-value (input) corresponds to exactly one \(y\)-value (output) are called functions. 10A visual representation of a relation on a rectangular coordinate plane. Given \(f (x) = 5x + 7\), find \(x\) where \(f (x) = 27\). Relations and functions class 11 worksheets with answers - There is Relations and functions class 11 worksheets with answers that can make the technique much. We have determined that the set of solutions to \(y = |x| 2\) is a function; therefore, using function notation we can write: \(\begin{aligned} y & = | x | - 2 \\ \color{Cerulean}{\downarrow} & \\ f ( x ) & = | x | - 2 \end{aligned}\). This is a coloring activity for a set of 12 problems on identifying the domain and range for a relation. Domain: \(\{5\}\); range: \(\{ 0,2,4,6,8 \}\); function: no, 7. Hence, the domain consists of all the real numbers in the set from \([1,5]\). The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds. Free to use Step-by-step explanations for every solution Exclusive how-to animations Sc. endobj
1. 120 students are studying in class 11 divided among four sections. Ans. We can visually identify functions by their graphs using the vertical line test15. Determine the domain and range of the following relation: The minimum \(x\)-value represented on the graph is \(8\) all others are larger. You can get arithmetic support online by visiting websites such as Khan Academy or by downloading apps such as Photomath. 33. g(x) = 2x + 1 Answer 34. g(x) = 5x 8 35. g(x) = 3x 2 Answer 36. g(x) = 8x + 2 37. g(x) = 3 x Answer 38. g(x) = 7 5x In the following exercises, evaluate the function. Not all relations are functions, and not all functions are relations. The student first takes notes on the definition of a relation and a function. If all these pointers match, then the relation is proved to be a function. Restart your browser. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? /F10 10 0 R Quizzes with auto-grading, and real-time student data. endobj
endobj
This is a relations and functions worksheet. If each input has only one line connected to it, then the outputs are a function of the . E6S2)212 "l+&Y4P%\%g|eTI (L 0_&l2E 9r9h xgIbifSb1+MxL0oE%YmhYh~S=zU&AYl/ $ZU m@O l^'lsk.+7o9V;?#I3eEKDd9i,UQ h6'~khu_ }9PIo= C#$n?z}[1 This product contains a worksheet and an assessment. endobj Here the compact notation \(f(5) = 3\) indicates that where \(x = 5\) (the input), the function results in \(y = 3\) (the output). 0000006193 00000 n
Given the graph of a function \(g\), find the \(x\)-values: 2. These multiple representation tasks help students see the connections between the equation, table of values, and graph. This is a multiple choice worksheet where students look at 20 different sets of relationships and decide yes or no rather the relationships are a function. 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. Functions are compactly defined by an algebraic equation, such as f(x) = | x | 2. 1. n 13 0 obj
It not only scans your equation and gives a mathematical answer, but it gives you reasoning behind how it's solved too! On the other hand, an undefined function is the one whose points are outside the domain. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. Relations and Functions Worksheet (with Answer Key + PDF) We can also recognize functions as relations where no \(x\)-values are repeated. xref
THIS APP IS THE BEST ONE EVER! A function, on the other hand, is a relation that produces one output for each given input. 2. Fast solutions. 13 0 obj Find \(x\) where \(g (x) = 0, g (x) = 10\), and \(g (x) = 15\). Given values for \(x\) in the domain, we can quickly calculate the corresponding values in the range. 7The four regions of a rectangular coordinate plane partly bounded by the \(x\)- and \(y\)-axes and numbered using the Roman numerals I, II, III, and IV. hs2z\nLA"Sdr%,lt As every value of x has a different value of y; it is a function.
1. The domain of the graph of \(x=|y|+1\) consists of all x-values greater than or equal to \(1, [1,)\), and the range consists of all real numbers, \(=(,)\). \(\begin{array} { c } { f ( x ) = 5 x + 7 }\\\color{Cerulean}{\downarrow}\quad\quad\quad\:\:\: \\ { 27 = 5 x + 7 } \\ { 20 = 5 x } \\ { 4 = x } \end{array}\). Range. A relation is any set of ordered pairs. 2 0 obj
Domain. If asked to find \(f(a)\), we substitute the argument \(a\) in for the variable and then simplify. Porque Es Malo Sentarse En La Puerta,
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Step 1: Tell the class a story involving a real-world, linear functional relationship. << Feel free to download and enjoy these free worksheets on functions and relations .Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Functions And Relations Worksheet | Teachers Pay Teachers Domain: \(\); range: \((, 3]\); function: yes, 21. If any vertical line intersects the graph more than once, then the graph does not represent a function. <> This worksheet is practice for the students on how to find the domain and range of a relation, decide if something is a function or not, and to express a relation using a table, graph, and mapping diagram. 4. In addition, since we can find a vertical line that intersects the graph more than once, we conclude that the graph is not a function. D \R(BJIBxCKoo-J-}wwfvv5s9["%VA This notation is used as follows: \(\begin{array} { l } { f ( x )\:\: =\:\:\: | x | - 2 } \\ { \:\:\:\:\:\downarrow \quad\quad\quad \downarrow } \\ { f ( \color{Cerulean}{- 5}\color{Black}{ )} = | \color{Cerulean}{- 5}\color{Black}{ |} - 2 = 5 - 2 = 3 } \end{array}\). So helpful with my homework. This relations functions worksheet may act as a last-minute tool to revise the function and relation problems before your exams. /Pattern << Reflections Over Intersecting Lines as Rotations. >> These two number lines define a flat surface called a plane4, and each point on this plane is associated with an ordered pair5 of real numbers \((x, y)\). /AIS false Worksheet 4.1 Relations and Functions Write each of the following as a relation, state the domain and range, then determine if it is a function. Relations Expressed as Graphing. The first 3 questions ask students to take a relation (given as a set of ordered pairs) and represent the relation as a table, graph, and mapping diagram. This assignment is also included in my:Algebra 1 Google Forms (, Functions and Relations Worksheets (Bundle), Relations, Functions, Domain and Range | Task Cards, Holt Algebra 4.2 Relations and Functions Worksheet DOC & PDF, Relations and Functions Worksheet (linear/non linear #2), Relations and Functions Notes and Worksheets, Relations and Functions Unit (Algebra 1 Unit 3), Functions and Linear Equations Quiz & Worksheet, Identifying Functions | Function or Not a Function Practice Worksheet, BACK TO SCHOOL | ALGEBRA 1 FUNCTIONS Bundle, Evaluating and Identifying Functions Worksheet, Relations and Functions Introduction Worksheets Bundle (Five Worksheets), Relations and Functions 2 (input-output boxes), Relations and Functions - Algebra 1 Skills Practice Worksheet, Algebra 1 Skills Practice Worksheets Bundle, Identifying Functions - Quick Coloring Activity, Domain and Range of Relations and Functions Quiz for Google Form/Quiz, Relations and Functions Worksheet (linear/non linear #1), RELATIONS AND FUNCTIONS: - IDENTIFY THE DOMAIN AND RANGE COLORING ACTIVITY # 2, Marie's Math Resources and Coloring Activities, Graphing Quadratic Functions in Standard Form Worksheets, Identifying Functions Independent Practice, Functions & Relations, Domain & Range Notes, Functions Unit Bundle - Algebra 1 Curriculum, Functions & Relations, Domain & Range, Function Notation Quiz, Daily Lessons in COMPARING & SORTING Preschool Lesson Plans, Algebra 1 Google Forms Semester 1 Digital Homework and Assessment Bundle. 3. Simplify \(\frac { q ( x + h ) - q ( x ) } { h }\) given \(q ( x ) = a x\). If f (x) = 2x 3, then find [f (0) + (f)] / 2 and value of x when (a) f(x) = 0 (b) f(x)= x and f(x) = f(1-x). d224f870063a40e098457059835651f2, 055c0d457aa04cdf98c57925f2da174b 8. 12 graphs.Worksheet 2: Finding range given domainRiddle. . New: \($22,000\); \(4\) years old: \($14,800\). Explore math program Students will find the range given the domain.Worksheet 3: Function rules and table of valuesStandard. I suggest using this as a note guide during the lesson. xwTS7" %z ;HQIP&vDF)VdTG"cEb PQDEk 5Yg} PtX4X\XffGD=H.d,P&s"7C$ <> 9. \(g ( - 3 ) = - 1 , g ( 0 ) = 1 , g ( 9 x + 6 ) = 6 x + 5\), 9. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> 12The set consisting of all of the second components of a relation. D 25. 0000001962 00000 n 3. This system is often called the Cartesian coordinate system8, named after the French mathematician Ren Descartes (15961650). 2. Relations and Functions Worksheet Answer Key 1. /XObject << If any vertical line intersects the graph more than once, then the graph does not represent a function. 4.0,` 3p H.Hi@A> Value of [f(0) + f(1)] / 2 is -2, (a) x = 3/2 (b) x = 3 (c) x = , 13. Domain and Range (Algebra 1) Here we separate the domain (x-values), and the range (y-values), and depict the correspondence between the values with arrows. Two Items Included. Determine the domain and range and state whether the relation is a function or not. 0000001084 00000 n 4.2 Relations and Functions A function is a relation in . O*?f`gC/O+FFGGz)~wgbk?J9mdwi?cOO?w| x&mf The intersection of the two axes is known as the origin6, which corresponds sto the point \((0, 0)\). Therefore, the domain consists of all \(x\)-values in the interval \([8,)\). 7. f(x) = x 8. h(x) = x + 7 9. g(x) = x - 2 10. g(x) = 3x 11. |E[v%D '_s;.C\{ b/01w$}1$>(EpyQx~_E6( yO-ve_v64> zR.,b EenTZU<8[o,T(%*pHB %ZqiCX|@B; -6c\)xN8} dgK|!OJn-)J8e1$>XFZk4:c[6\0dY4i\W+H}#s.v.9_ 6!jW3bsFqPYb:h C8Ejp3+t 1,WC?d`}!*/V;7j @T1yDF,5M=]nOnD; Given the linear function defined by \(f(x)=2x-5\), simplify the following. A function is a relation in which each possible input value leads to exactly one output value. Research and discuss the life and contributions of Ren Descartes. 14. Range: Function: o 2 t 3 3 (3, 3) -2) Relation . Worksheet 4.1 relations and functions answer key. endobj Then they share a relationship and can be written as an ordered pair (x, y). 1. Given \(f ( x ) = \sqrt { 2 x + 4 }\), find \(f (2), f (0)\), and \(f \left( \frac { 1 } { 2 } a ^ { 2 } - 2 \right)\). Chapter 3: Introduction to Functions and Relations. >> Section 3.1. The minimum \(y\)-value represented on the graph is \(0\); thus, the range is \([0,)\). /CreationDate (D:20220708141653-04'00') Domain: \((, 0]\); range: \([1, )\); function: yes, 19. 15 33 17 15, 11 15 Relations Expressed as Graphing Write each of the following as a relation, state the domain and range, then determine if it is a function. Download Relations and Functions Worksheet PDFs These math worksheets should be practiced regularly and are free to download in PDF formats. %%EOF \(f ( - 1 ) = 0 , f ( 0 ) = 1 , f \left( a ^ { 2 } \right) = a ^ { 6 } + 1\), 3. >> Write each of the following as a relation, state the domain and range, then determine if it is a function. {(3,2), (1, -1), (2, -4), (3, -9), (4, -16)} 4. Posted: 7/3/17 so 50% off through 7/6/17, Do your students need practice graphing real world quadratics? RELATIONS & FUNCTIONS Worksheet. Feel free to download and enjoy these free worksheets on functions and relations. Determine the domain and range of the following relation and state whether it is a function or not: \(\{(4, 3), (2, 6), (0, 3), (3, 5), (3, 7)\}\). 12. Included are 5 different task sheets. For instance, f(x) = root over x is an undefined function when the value of x is negative. Evaluate the inverse and also rule out whether the same is a function or not. Share a link to a page that you think others may find useful. <> 16The notation \(f (x) = y\), which reads \(f\) of \(x\) is equal to \(y\). Given a function, \(y\) and \(f (x)\) can be used interchangeably. Explain. [ -c R!z"^Ow,c 2The horizontal number line used as reference in a rectangular coordinate system. How to Determine Whether a Given Relation is a Function or Not? Special relations where every \(x\)-value (input) corresponds to exactly one \(y\)-value (output) are called functions. 10A visual representation of a relation on a rectangular coordinate plane. Given \(f (x) = 5x + 7\), find \(x\) where \(f (x) = 27\). Relations and functions class 11 worksheets with answers - There is Relations and functions class 11 worksheets with answers that can make the technique much. We have determined that the set of solutions to \(y = |x| 2\) is a function; therefore, using function notation we can write: \(\begin{aligned} y & = | x | - 2 \\ \color{Cerulean}{\downarrow} & \\ f ( x ) & = | x | - 2 \end{aligned}\). This is a coloring activity for a set of 12 problems on identifying the domain and range for a relation. Domain: \(\{5\}\); range: \(\{ 0,2,4,6,8 \}\); function: no, 7. Hence, the domain consists of all the real numbers in the set from \([1,5]\). The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds. Free to use Step-by-step explanations for every solution Exclusive how-to animations Sc. endobj 1. 120 students are studying in class 11 divided among four sections. Ans. We can visually identify functions by their graphs using the vertical line test15. Determine the domain and range of the following relation: The minimum \(x\)-value represented on the graph is \(8\) all others are larger. You can get arithmetic support online by visiting websites such as Khan Academy or by downloading apps such as Photomath. 33. g(x) = 2x + 1 Answer 34. g(x) = 5x 8 35. g(x) = 3x 2 Answer 36. g(x) = 8x + 2 37. g(x) = 3 x Answer 38. g(x) = 7 5x In the following exercises, evaluate the function. Not all relations are functions, and not all functions are relations. The student first takes notes on the definition of a relation and a function. If all these pointers match, then the relation is proved to be a function. Restart your browser. Are you getting the free resources, updates, and special offers we send out every week in our teacher newsletter? /F10 10 0 R Quizzes with auto-grading, and real-time student data. endobj endobj This is a relations and functions worksheet. If each input has only one line connected to it, then the outputs are a function of the . E6S2)212 "l+&Y4P%\%g|eTI (L 0_&l2E 9r9h xgIbifSb1+MxL0oE%YmhYh~S=zU&AYl/ $ZU m@O l^'lsk.+7o9V;?#I3eEKDd9i,UQ h6'~khu_ }9PIo= C#$n?z}[1 This product contains a worksheet and an assessment. endobj Here the compact notation \(f(5) = 3\) indicates that where \(x = 5\) (the input), the function results in \(y = 3\) (the output). 0000006193 00000 n Given the graph of a function \(g\), find the \(x\)-values: 2. These multiple representation tasks help students see the connections between the equation, table of values, and graph. This is a multiple choice worksheet where students look at 20 different sets of relationships and decide yes or no rather the relationships are a function. 3. f-1 (x) = (9x/5) + 32 and the inverse is a function also. Functions are compactly defined by an algebraic equation, such as f(x) = | x | 2. 1. n 13 0 obj It not only scans your equation and gives a mathematical answer, but it gives you reasoning behind how it's solved too! On the other hand, an undefined function is the one whose points are outside the domain. Algebra 2 relations and functions worksheet answers can be a useful tool for these scholars. Relations and Functions Worksheet (with Answer Key + PDF) We can also recognize functions as relations where no \(x\)-values are repeated. xref THIS APP IS THE BEST ONE EVER! A function, on the other hand, is a relation that produces one output for each given input. 2. Fast solutions. 13 0 obj Find \(x\) where \(g (x) = 0, g (x) = 10\), and \(g (x) = 15\). Given values for \(x\) in the domain, we can quickly calculate the corresponding values in the range. 7The four regions of a rectangular coordinate plane partly bounded by the \(x\)- and \(y\)-axes and numbered using the Roman numerals I, II, III, and IV. hs2z\nLA"Sdr%,lt As every value of x has a different value of y; it is a function. 1. The domain of the graph of \(x=|y|+1\) consists of all x-values greater than or equal to \(1, [1,)\), and the range consists of all real numbers, \(=(,)\). \(\begin{array} { c } { f ( x ) = 5 x + 7 }\\\color{Cerulean}{\downarrow}\quad\quad\quad\:\:\: \\ { 27 = 5 x + 7 } \\ { 20 = 5 x } \\ { 4 = x } \end{array}\). Range. A relation is any set of ordered pairs. 2 0 obj Domain. If asked to find \(f(a)\), we substitute the argument \(a\) in for the variable and then simplify.