Chapter 3 Maintaining Mathematical Proficiency

Name DateChapterMaintaining Mathematical Proficiency3Plot the point in a coordinate plane. Describe the location of the point.1. A( 3, 1)2. B ( 2, 2)y3. C (1, 0)y2y2 22x 2 24. D (5, 2)y22x 2 222x 224x 25. Plot the point that is on the y-axis and 5 units down from the origin.y 22x 2 4Evaluate the expression for the given value of x.6. 2 x 1; x 37. 16 4 x; x 48. 12 x 7; x 29. 9 3x; x 510. The length of a side of a square is represented by ( 24 3 x ) feet. What is thelength of the side of the square when x 6?58Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.

NameDateFunctions3.1For use with Exploration 3.1Essential Question What is a function?1EXPLORATION: Describing a FunctionWork with a partner. Functions can be described in many ways.y by an equation by an input-output table using words by a graph as a set of ordered pairs8642002468xa. Explain why the graph shown represents a function.b. Describe the function in two other ways.2EXPLORATION: Identifying FunctionsWork with a partner. Determine whether each relation represents a function. Explainyour reasoning.a.b.Input, x01234Output, y88888Input, x88888Output, y01234Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal59

Name Date3.12Functions (continued)EXPLORATION: Identifying Functions (continued)c.Input, x Output, y123d.y88910116420e.( 2, 5), ( 1, 8), (0, 6), (1, 6), (2, 7)f.02468x( 2, 0), ( 1, 0), ( 1, 1), (0, 1), (1, 2), (2, 2)g. Each radio frequency x in a listening area has exactly one radio station y.h. The same television station x can be found on more than one channel y.i. x 2j.y 2x 3Communicate Your Answer3. What is a function? Give examples of relations, other than those in Explorations 1and 2, that (a) are functions and (b) are not functions.60Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.1DateNotetaking with VocabularyFor use after Lesson 3.1In your own words, write the meaning of each vocabulary term.relationfunctiondomainrangeindependent variabledependent variableNotes:Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal61

Name Date3.1Notetaking with Vocabulary (continued)Core ConceptsVertical Line TestWords A graph represent a function when no vertical line passes through more than onepoint on the graph.Examples FunctionNot a functionyyxxNotes:The Domain and Range of a FunctionThe domain of a function is the set of all possible input values.The range of a function is the set of all possible output values.input 2 6outputNotes:62Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.1DateNotetaking with Vocabulary (continued)Extra PracticeIn Exercises 1 and 2, determine whether the relation is a function. Explain.1.Input, x–201–2Output, y45452.(0, 3), (1, 1), (2, 1), (3, 0)In Exercises 3 and 4, determine whether the graph represents a function. Explain.3.4.y6y44220 20242x6 xIn Exercises 5 and 6, find the domain and range of the function represented by thegraph.5.6.y642420y 20246 x2x 27. The function y 12 x represents the number y of pages of text a computer printer can printin x minutes.a. Identify the independent and dependent variables.b. The domain is 1, 2, 3, and 4. What is the range?Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal63

Name DateLinear Functions3.2For use with Exploration 3.2Essential Question How can you determine whether a function is linearor nonlinear?1EXPLORATION: Finding Patterns for Similar FiguresGo to BigIdeasMath.com for an interactive tool to investigate this exploration.Work with a partner. Complete each table for the sequence of similar figures. (In parts(a) and (b), use the rectangle shown.) Graph the data in each table. Decide whether eachpattern is linear or nonlinear. Justify your conclusion.x2xa. perimeters of similar rectanglesx2345xPAPA40403030202010100641b. areas of similar rectangles02Algebra 1Student Journal468x00122344658xCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.21DateLinear Functions (continued)EXPLORATION: Finding Patterns for Similar Figures (continued)c. circumferences of circles of radius rr12345d. areas of circles of radius te Your Answer2. How do you know that the patterns you found in Exploration 1 representfunctions?3. How can you determine whether a function is linear or nonlinear?4. Describe two real-life patterns: one that is linear and one that is nonlinear. Usepatterns that are different from those described in Exploration 1.Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal65

Name Date3.2Notetaking with VocabularyFor use after Lesson 3.2In your own words, write the meaning of each vocabulary term.linear equation in two variableslinear functionnonlinear functionsolution of a linear equation in two variablesdiscrete domaincontinuous domainNotes:66Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.2DateNotetaking with Vocabulary (continued)Core ConceptsRepresentations of FunctionsWords An output is 3 more than the input.Equation y x 3Input-Output TableMapping DiagramInput, xOutput, yInput, xOutput, y 12031425 10122345Graph6y42 224 xNotes:Discrete and Continuous DomainsA discrete domain is a set of input values that consists of only certain numbers in an interval.Example: Integers from 1 to 5 2 10123456A continuous domain is a set of input values that consists of all numbers in an interval.Example: All numbers from 1 to 5 2 10123456Notes:Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal67

Name Date3.2Notetaking with Vocabulary (continued)Extra PracticeIn Exercises 1 and 2, determine whether the graph represents a linear or nonlinearfunction. Explain.1.42.yy222246 xx 2In Exercises 3 and 4, determine whether the table represents a linear or nonlinearfunction. Explain.3.x1234y–12584.x–1012y0–103In Exercises 5 and 6, determine whether the equation represents a linear ornonlinear function. Explain.6. y 3 x 345. y 3 2 xIn Exercises 7 and 8, find the domain of the function represented by the graph.Determine whether the domain is discrete or continuous. Explain.7.68.y442226864Algebra 1Student Journal6 xy246 xCopyright Big Ideas Learning, LLCAll rights reserved.

NameDateFunction Notation3.3For use with Exploration 3.3Essential Question How can you use function notation to represent afunction?1EXPLORATION: Matching Functions with Their GraphsWork with a partner. Match each function with its graph.a.f ( x) 2 x 3b. g ( x) x 2c. h( x) x 2 1d.4A. 6j ( x) 2 x 2 3B.64 6 4 44C. 6D.6 4Copyright Big Ideas Learning, LLCAll rights reserved.64 66 4Algebra 1Student Journal69

Name Date3.32Function Notation (continued)EXPLORATION: Evaluating a FunctionGo to BigIdeasMath.com for an interactive tool to investigate this exploration.Work with a partner. Consider the function5f(x) x 3f ( x) x 3.Locate the points ( x, f ( x)) on the graph. 6Explain how you found each point.a.( 1, f ( 1))b.(0, f (0))c.(1, f (1))d.(2, f (2))6 3Communicate Your Answer3. How can you use function notation to represent a function? How are standardnotation and function notation similar? How are they different?70Standard NotationFunction Notationy 2x 5f ( x) 2 x 5Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.3DateNotetaking with VocabularyFor use after Lesson 3.3In your own words, write the meaning of each vocabulary term.function notationNotes:Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal71

Name Date3.3Notetaking with Vocabulary (continued)Extra PracticeIn Exercises 1–6, evaluate the function when x 4, 0, and 2.1.f ( x) x 44. s ( x) 12 0.25 x2. g ( x) 5 x3. h( x) 7 2 x5. t ( x) 6 3 x 26. u ( x) 2 2 x 77. Let n(t ) be the number of DVDs you have in your collection after t trips to the video store. Explainthe meaning of each statement.a. n(0) 8b. n(3) 14c. n(5) n(3)d. n(7) n( 2) 10In Exercises 8–11, find the value of x so that the function has the given value.8. b( x) 3 x 1; b ( x) 2010. m( x) 3 x 4; m( x) 2572Algebra 1Student Journal9. r ( x) 4 x 3; r ( x) 3311. w( x) 5 x 3; w( x) 186Copyright Big Ideas Learning, LLCAll rights reserved.

Name3.3DateNotetaking with Vocabulary (continued)In Exercises 12 and 13, graph the linear function.12. s ( x) 1 x 22x–413. t ( x) 1 2 x–202s(x)4x–2012t (x)4y42 4–1 2y224 x 4 22 2 2 4 414. The function B ( m) 50m 150 represents the balance(in dollars) in your savings account after m months. Thetable shows the balance in your friend's savings account.Who has the better savings plan? Explain.Copyright Big Ideas Learning, LLCAll rights reserved.4 xMonthBalance2 3304 4106 490Algebra 1Student Journal73

Name DateGraphing Linear Equations in Standard Form3.4For use with Exploration 3.4Essential Question How can you describe the graph of the equationAx By C ?1EXPLORATION: Using a Table to Plot PointsGo to BigIdeasMath.com for an interactive tool to investigate this exploration.Work with a partner. You sold a total of 16 worth of tickets to a fundraiser. You losttrack of how many of each type of ticket you sold. Adult tickets are 4 each. Childtickets are 2 each. adultNumber of adult ticketschild Number of child ticketsa. Let x represent the number of adult tickets. Let y represent the number of childtickets. Use the verbal model to write an equation that relates x and y.b. Complete the table to showthe different combinations oftickets you might have sold.xyc. Plot the points from the table. Describe the pattern formed by the points.8y6422468 xd. If you remember how many adult tickets you sold, can you determine how manychild tickets you sold? Explain your reasoning.74Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.

Name3.42DateGraphing Linear Equations in Standard Form (continued)EXPLORATION: Rewriting and Graphing an EquationGo to BigIdeasMath.com for an interactive tool to investigate this exploration.Work with a partner. You sold a total of 48 worth of cheese. You forgot how manypounds of each type of cheese you sold. Swiss cheese costs 8 per pound. Cheddarcheese costs 6 per pound.pound Pounds ofSwiss pound Pounds ofcheddar a. Let x represent the number of pounds of Swiss cheese. Let y represent the numberof pounds of cheddar cheese. Use the verbal model to write an equation thatrelates x and y.b. Solve the equation for y. Then use a graphing calculator to graph the equation.Given the real-life context of the problem, find the domain and range of thefunction.c. The x-intercept of a graph is the x-coordinate of a point where the graph crossesthe x-axis. The y-intercept of a graph is the y-coordinate of a point where thegraph crosses the y-axis. Use the graph to determine the x- and y-intercepts.d. How could you use the equation you found in part (a) to determine thex- and y-intercepts? Explain your reasoning.e. Explain the meaning of the intercepts in the context of the problem.Communicate Your Answer3. How can you describe the graph of the equation Ax By C ?4. Write a real-life problem that is similar to those shown in Explorations 1 and 2.Copyright Big Ideas Learning, LLCAll rights reserved.Algebra 1Student Journal75

Name DateNotetaking with Vocabulary3.4For use after Lesson 3.4In your own words, write the meaning of each vocabulary term.standard formx-intercepty-interceptCore ConceptsHorizontal and Vertical Linesyyy bx a(0, b)(a, 0)xxThe graph of y b is a horizontal line.The graph of x a is a vertical line.The line passes through the point (0, b).The line passes through the point ( a, 0).Notes:76Algebra 1Student JournalCopyright Big Ideas Learning, LLCAll rights reserved.