2.1 Represent Relations and
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1 . Represent Relations and Functions Goal p Represent relations and graph linear functions. Your Notes VOCABULARY Relation Domain Range Function Equation in two variables Linear function REPRESENTING RELATIONS A relation can be represented in the following was: Ordered Table Graph Mapping Pairs Diagram (, ) Input (, ) (, ) (, ) Output 8 Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.
2 . Represent Relations and Functions Goal p Represent relations and graph linear functions. Your Notes VOCABULARY Relation A mapping, or pairing, of input values with output values Domain The set of input values in a relation Range The set of output values in a relation Function A relation for which each input has eactl one output Equation in two variables An equation that has an independent or input variable and a dependent or output variable that depends on the value of the input variable Linear function A function that can be written in the form 5 m b, where m and b are constants REPRESENTING RELATIONS A relation can be represented in the following was: Ordered Table Graph Mapping Pairs Diagram (, ) Input (, ) (, ) (, ) Output 8 Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.
3 Eample Tell whether each relation is a function. Eplain. a. Input Output b. Input Output 6 Identif functions 4 a. The relation a function because each input is mapped onto output. b. The relation a function because the input is mapped onto and. Checkpoint Complete the following eercise.. Is the relation given b the ordered pairs (5, ), (, ), (, ), (, ) and (, 5) a function? Eplain. VERTICAL LINE TEST A relation is a function if and onl if no line intersects the graph of the relation at more than. Function Not a function Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide 9
4 Eample Tell whether each relation is a function. Eplain. a. Input Output b. Input Output 6 Identif functions 4 a. The relation is a function because each input is mapped onto eactl one output. b. The relation is not a function because the input is mapped onto and. Checkpoint Complete the following eercise.. Is the relation given b the ordered pairs (5, ), (, ), (, ), (, ) and (, 5) a function? Eplain. No, the relation is not a function because the value maps to,, and 5. VERTICAL LINE TEST A relation is a function if and onl if no vertical line intersects the graph of the relation at more than one point. Function Not a function Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide 9
5 Eample Use the vertical line test Is the relation represented b the graph a function? Eplain. a. b. a. This graph represent a function because no vertical line intersects the graph at more than. b. This graph represent a function because the vertical lines at 5 and at 5 intersect the graph at more than one point. GRAPHING EQUATIONS IN TWO VARIABLES To graph an equation in two variables, follow these steps: Step Construct a table of. Step Plot enough points from the table to recognize a. Step Connect the points with a or. Eample Graph an equation in two variables Graph the equation 5. Step Construct a table of values. Step Plot the points. Notice that the all lie on a. Step the points with a line. Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.
6 Eample Use the vertical line test Is the relation represented b the graph a function? Eplain. a. b. a. This graph does represent a function because no vertical line intersects the graph at more than one point. b. This graph does not represent a function because the vertical lines at 5 and at 5 6 intersect the graph at more than one point. GRAPHING EQUATIONS IN TWO VARIABLES To graph an equation in two variables, follow these steps: Step Construct a table of values. Step Plot enough points from the table to recognize a pattern. Step Connect the points with a line or curve. Eample Graph an equation in two variables Graph the equation 5. Step Construct a table of values. 4 6 Step Plot the points. Notice that the all lie on a line. Step Connect the points with a line. Lesson. Algebra Notetaking Guide Copright Holt McDougal. All rights reserved.
7 Eample 4 Classif and evaluate functions Tell whether the function is linear. Then evaluate the function when 5. a. f() 5 6 b. g() 5 4 a. The function f is because it has the form f() 5 m b. f() 5 6 Write function. f( ) 5 6( ) Substitute for. 5 Simplif. b. The function g is because it has an -term. g() 5 4 Write function. g( ) 5 ( ) 4( ) Substitute for. 5 Simplif. Checkpoint Complete the following eercises.. Use the vertical line test. Graph the equation to tell whether the 5. relation is a function. Homework Tell whether the function is linear. Then evaluate the function when f() g() Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide
8 Eample 4 Classif and evaluate functions Tell whether the function is linear. Then evaluate the function when 5. a. f() 5 6 b. g() 5 4 a. The function f is linear because it has the form f() 5 m b. f() 5 6 Write function. f( ) 5 6( ) Substitute for. 5 8 Simplif. b. The function g is not linear because it has an -term. g() 5 4 Write function. g( ) 5 ( ) 4( ) Substitute for. 5 5 Simplif. Checkpoint Complete the following eercises.. Use the vertical line test. Graph the equation to tell whether the 5. relation is a function. is a function Homework Tell whether the function is linear. Then evaluate the function when f() g() not linear; 5 linear; 5 Copright Holt McDougal. All rights reserved. Lesson. Algebra Notetaking Guide
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