Vocabulary. Term Page Definition Clarifying Example. dependent variable. domain. function. independent variable. parent function.

Transcription

1 CHAPTER 1 Vocabular The table contains important vocabular terms from Chapter 1. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. dependent variable Term Page Definition Clarifing Eample domain function independent variable parent function principal root radicand Algebra

2 CHAPTER 1 Vocabular The table contains important vocabular terms from Chapter 1. As ou work through the chapter, fill in the page number, definition, and a clarifing eample. Term Page Definition Clarifing Eample dependent variable domain function independent variable parent function The output of a function; a variable whose value depends on the value of the input, or independent variable. The set of all possible input values of a relation or function. A relation in which ever input is paired with eactl one output. The input of a function; a variable whose value determines the value of the output, or dependent variable. The simplest function with the defining characteristics of the famil. Functions in the same famil are transformations of their parent function. For 1, is the dependent variable. The domain of the function f() is { 0}. Function: {(0, 5), (1, 3), (, 1)} Not a function: {(0, 1), (0, 3), (, 1)} For 1, is the independent variable. f() is the parent function for g() and h() 5( ) 3 principal root radicand 1 1 The positive root of a number, indicated b the radical sign. The epression under a radical sign. 36 has two square roots, 6 and 6. The principal square root of 36 is Epression: 3 Radicand: 3 Algebra

3 CHAPTER 1 VOCABULARY CONTINUED reflection Term Page Definition Clarifing Eample relation scientific notation set set-builder notation subset transformation translation 5 Algebra

4 CHAPTER 1 VOCABULARY CONTINUED Term Page Definition Clarifing Eample reflection relation scientific notation set set-builder notation subset transformation translation A transformation that reflects, or flips, a graph or figure across a line, called the line of reflection, such that each reflected point is the same distance from the line of reflection but is on the opposite side of the line. A set of ordered pairs. A method of writing ver large or ver small numbers, b using powers of 10, in the form m 10 n, where 1 m 10 and n is an integer. A collection of items called elements. A notation for a set that uses a rule to describe the properties of the elements of the set. A set that is contained entirel within another set. Set B is a subset of set A if ever element of B is contained in A, denoted B A. A change in the position, size, or shape of a figure or graph A transformation that shifts or slides ever point of a figure or graph the same distance in the same direction. {(0, 5), (0, ), (, 3), (, 0)} 1,560,000, {1,, 3} 0 { 3} is read The set of all such that is greater than 3. The set of integers is a subset of the set of rational numbers, denoted 0 3 f 5 Algebra

5 CHAPTER 1 Chapter Review 1-1 Sets of Numbers Order the given numbers from least to greatest. Then classif each number b the subsets of the real numbers to which it belongs , 1,.15, , 7, 1, Rewrite each set in the indicated notation. 11. { }; 1. ; interval notation set-builder notation 1- Properties of Real Numbers Identif the propert demonstrated b each equation. 13. t t 1. a (6 ) (a 6) 15. a b (a b) Use mental math to find a 5% discount on an item that costs $160. Eplain our steps. Algebra

6 CHAPTER 1 Chapter Review 1-1 Sets of Numbers Order the given numbers from least to greatest. Then classif each number b the subsets of the real numbers to which it belongs , 1,.15, , 3.66, 1, rational; real rational; real. 1 irrational; real 6. 10, 7, 1, , 3, 1 5, rational; real irrational; real rational; real whole; integer; rational; 9. 7 real integer; rational; real Rewrite each set in the indicated notation. 11. { }; 1. ; interval notation set-builder notation (, ) { 3 } 1- Properties of Real Numbers Identif the propert demonstrated b each equation. 13. t t 1. a (6 ) (a 6) Commutative Propert of Addition Associative Propert of Addition 15. a b (a b) Distributive Propert Identit Propert of Zero 17. Use mental math to find a 5% discount on an item that costs $160. Eplain our steps. $0; Sample answer: 5% 10% 10% 5%; 10% of $160 is $16 and 5% is $8. $16 $16 $8 $0 Algebra

7 CHAPTER 1 REVIEW CONTINUED 1-3 Square Roots 18. Margaret is putting baseboard around the bottom edge of a square-shaped room. The room is 196 ft. If the baseboard comes in lengths of 10 feet, how man pieces of baseboard should she bu to place baseboard around the entire room? Simplif each epression Simplifing Algebraic Epressions Evaluate each epression for the given values of the variables. 3. 1ab ab for a 3 and b. ab for a and b 3 5a b Simplif each epression ( ) Properties of Eponents Simplif each epression. Assume all variables are nonzero a b 3ab 9. 6(m n 3 ) One parasec is about 3.6 light-ears and 1 light-ear is about miles. Find the number of miles in one parasec. 5 Algebra

8 CHAPTER 1 REVIEW CONTINUED 1-3 Square Roots 18. Margaret is putting baseboard around the bottom edge of a square-shaped room. The room is 196 ft. If the baseboard comes in lengths of 10 feet, how man pieces of baseboard should she bu to place baseboard around the entire room? 6 pieces Simplif each epression Simplifing Algebraic Epressions Evaluate each epression for the given values of the variables. 3. 1ab ab for a 3 and b. ab for a and b 3 5a b Simplif each epression ( ) Properties of Eponents Simplif each epression. Assume all variables are nonzero or a b 3ab 6m 6 n 9 6 or 9. 6(m n 3 ) m 6 n One parasec is about 3.6 light-ears and 1 light-ear is about miles. Find the number of miles in one parasec. b 6 a Algebra

9 CHAPTER 1 REVIEW CONTINUED 1-6 Relations and Functions Give the domain and range for each relation. Then tell whether the relation is a function Perimeter of Area of Square Square Function Notation For each function, determine f( 1), f(0), and f(). 35. f() 36. f() f() A wood planer costs $1.50 to turn on and $0.75 per minute of use. a. Write a function to represent the cost of the wood planer per number of minutes used. 6 Algebra

10 CHAPTER 1 REVIEW CONTINUED 1-6 Relations and Functions Give the domain and range for each relation. Then tell whether the relation is a function Perimeter of Area of Square Square Domain: {,, 6, 8}; Range: {1, }; es Domain: {, 8, 1, 16}; Range: {1,, 9, 16}; es 3. Domain: { 1, 0, 1}; Range: {, 0, 1, 3, }; No 1-7 Function Notation For each function, determine f( 1), f(0), and f(). 35. f() 36. f() f() 3 1; ; 0 9; 8; 0 7; ; 38. A wood planer costs $1.50 to turn on and $0.75 per minute of use. a. Write a function to represent the cost of the wood planer per number of minutes used. c(t) 0.75t Algebra

11 CHAPTER 1 REVIEW CONTINUED b. Graph the function. c. Give the value of the function for an input of 1 and eplain its real-world meaning. 1-8 Eploring Transformations 39. Use a table to perform the transformation of f(). Graph the transformed function on the same coordinate plane as the original function. translation up 3 units The graph shows the gross pa that ou would make working a particular number of hours per week. Sketch a graph to represent an hourl rate increase of $1 per hour and identif the transformation of the original graph that it represents Algebra

12 CHAPTER 1 REVIEW CONTINUED b. Graph the function. c. Give the value of the function for an input of 1 and eplain its real-world meaning. c(1) $10.50; It is the cost of using the wood planer for 1 minutes. 1-8 Eploring Transformations 39. Use a table to perform the transformation of f(). Graph the transformed function on the same coordinate plane as the original function. translation up 3 units The graph shows the gross pa that ou would make working a particular number of hours per week. Sketch a graph to represent an hourl rate increase of $1 per hour and identif the transformation of the original graph that it represents Algebra

13 CHAPTER 1 REVIEW CONTINUED 1-9 Introduction to Parent Functions Identif the parent function for g from its equation. Then graph g on our calculator and describe what transformation of the parent function it represents. 1. g() 3. g() g() 1 3. Graph the relationship between the number of minutes spent studing and the score on the math quiz. Identif which parent function best describes the data. Then use the graph to estimate the score on a quiz when 0 minutes are spent studing. Minutes Studing Score of Math Quiz 8 Algebra

14 CHAPTER 1 REVIEW CONTINUED 1-9 Introduction to Parent Functions Identif the parent function for g from its equation. Then graph g on our calculator and describe what transformation of the parent function it represents. 1. g() 3. g() 3 1 ; units down, stretched verticall b a factor of 3 3 ; 1 unit up ; 3 units down, stretched 3. g() 1 3 verticall b a factor of 1.. Graph the relationship between the number of minutes spent studing and the score on the math quiz. Identif which parent function best describes the data. Then use the graph to estimate the score on a quiz when 0 minutes are spent studing. Minutes Studing Score of Math Quiz The parent function is A score of 8 would be epected with 0 minutes of studing. 8 Algebra

15 CHAPTER 1 Big Ideas Answer these questions to summarize the important concepts from Chapter 1 in our own words. 1. Eplain how the various sets of numbers are related.. Eplain how the Additive Inverse Propert differs from the Multiplicative Inverse Propert. 3. Eplain how to simplif an algebraic epression.. What makes a relation a function? Eplain how the inputs and outputs of a function are related. For more review of Chapter 1: Complete the Chapter 1 Stud Guide and Review on pages of our tetbook. Complete the Read to Go On quizzes on pages 3 and 75 of our tetbook. 9 Algebra

16 CHAPTER 1 Big Ideas Answer these questions to summarize the important concepts from Chapter 1 in our own words. 1. Eplain how the various sets of numbers are related. Real Numbers consist of Rational Numbers and Irrational Numbers. The Rational Numbers consist of Integers, Whole Numbers, and Natural Numbers. Eplain how the Additive Inverse Propert differs from the Multiplicative Inverse Propert. The Additive Inverse Propert states that the sum of a number and its opposite is 0. The Multiplicative Inverse Propert states the product of a nonzero number and its reciprocal is Eplain how to simplif an algebraic epression. To simplif an algebraic epression, combine like terms b adding or subtracting the coefficients. Like terms have the same eponent raised to the same power.. What makes a relation a function? Eplain how the inputs and outputs of a function are related. A relation in which the first coordinate is never repeated is called a function. A function has onl one output for each input, so each element of the domain is mapped to eactl one element in the range. Even though a function cannot map a single input to more than one output, two or more different inputs can be mapped to the same output. For more review of Chapter 1: Complete the Chapter 1 Stud Guide and Review on pages of our tetbook. Complete the Read to Go On quizzes on pages 3 and 75 of our tetbook. 9 Algebra