Developed in Consultation with Tennessee Educators

Developed in Consultation with Tennessee Educators

Table of Contents Letter to the Student........................................ Test-Taking Checklist........................................ Tennessee State Performance Indicators Correlation Chart........ 7 Tennessee State Performance Indicators Chapter Number and Operations.......................... Lesson Rational and Irrational Numbers............. Lesson Radicals............................. 7.. Lesson Operations with Radicals.................. Lesson Operations with Numbers in Scientific Notation..................... 7.. Chapter Review............................ Chapter Algebra: Patterns, Polnomials, and Epressions.... 7 Lesson Patterns............................. 8..,.. Lesson Adding and Subtracting Polnomials......... Lesson 7 Multipling and Dividing Polnomials....... 7.. Lesson 8 Factoring Polnomials.................... Lesson 9 Rational Epressions................... 9.. Lesson Evaluating Epressions....................,..7 Chapter Review............................ 9 Chapter Algebra: Equations, Inequalities, and Functions..... 7 Lesson Identifing Functions................... 7..,..7 Lesson Domain, Range, and Function Notation..... 8..,..,..,........................................................7 Lesson Writing and Solving Linear Equations....... 8..,.. Lesson Writing and Solving Linear Inequalities...... 9.. Lesson Solving Absolute Value Equations and Inequalities........................ 98.. Lesson Graphing and Writing Equations of a Line.....,..,..8 Lesson 7 Solving Sstems of Linear Equations Graphicall............................9 Duplicating an part of this book is prohibited b law.

Lesson 8 Solving Sstems of Linear Equations Algebraicall...........................9 Lesson 9 Solving Sstems of Linear Inequalities.......9 Lesson Solving Quadratic Equations Algebraicall.. 8.. Lesson Solving Quadratic Functions Graphicall..... Lesson Analzing Nonlinear Graphs...............,.. Chapter Review........................... Chapter Geometr and Measurement.................... Lesson Estimating the Area of Shapes............. Lesson Problem Solving with the Pthagorean Theorem................. 8..,.. Lesson Distance and Midpoint................... Lesson Converting Rates and Measurements..... 8.. Chapter Review............................ 7 Chapter Data Analsis, Statistics, and Probabilit........... 77 Lesson 7 Data Displas........................ 78.. Lesson 8 Changing Values in a Set of Data......... 8.. Lesson 9 Scatter-Plots and Lines of Best Fit........ 9..,..,.. Lesson Probabilit........................... 9.. Lesson Relative Frequenc...................... Chapter Review............................ 7 Glossar................................................. Duplicating an part of this book is prohibited b law.

Identifing Functions..,..7 In the table below, the numbers in the rows represent coordinates: (, ), (, ), (, ), (, ), (, ), (, 9), and (, 9). The relationship between the numbers is represented b the equation. When ou square the first number in the ordered pair, the result is the second number in the ordered pair. The graph below shows the coordinates in the table plotted on the grid and connected with a smooth curve. 9 9 9 8 7 8 7 7 8 9 7 8 9 9 A relation is a set of ordered pairs that connects a set of output numbers, or -values, to a set of input numbers, or -values. A function is a relation in which each input number, or -value, has one and onl one output number, or -value. The table and graph above represent a function. For each -value, there is one and onl one -value. 7 Duplicating an part of this book is prohibited b law.

Lesson : Identifing Functions You can use the vertical line test to determine if a graph represents a function. If there are no vertical lines that intersect the graph in more than one point, then the graph represents a function. The graph on the left below is a function. The dashed vertical lines each intersect the graph in eactl one point. That is, each input () value corresponds to one and onl one output () value. The graph on the right below is not a function because at least one dashed vertical line intersects the graph at more than one point. That is, there is at least one -value that has more than one -value. a function not a function EXAMPLE Is the relation represented in the table a function? STRATEGY STEP STEP SOLUTION Compare the - and -values. If each -value has one and onl one -value, then the relation is a function. Compare - and -values. has the -values of and. has the -values of and. has a -value of. Does an -value have more than one -value? Both and have more than one -value. The relation is not a function. Duplicating an part of this book is prohibited b law. 7

If a relation is given as a set of ordered pairs, ou can determine whether it is a function b looking at the -coordinates. If an of the ordered pairs have the same -coordinate but different -coordinates, then the relation is not a function. For eample, ou can write the table of values in Eample as a set of ordered pairs. (, ), (, ), (, ), (, ), (, ) The relation is not a function because both and appear more than once as -coordinates. EXAMPLE Classif each relation as a function or not a function.. (, ), (, 9), (, ), (8, 7), (, ). (, ), (, 9), (, ), (, ), (, ) STRATEGY STEP STEP SOLUTION Check each set with the definition of function. Check the first set. The -coordinate is repeated, but none of the -coordinates is repeated. So, each -coordinate has one and onl one -coordinate. The relation is a function. Check the second set. None of the -coordinates is repeated, but the -coordinate is repeated. The -coordinate has the -coordinates 9 and. The relation is not a function. The first relation is a function; the second is not a function. Another wa to determine if a relation is a function is with a mapping. In a mapping, each -value is mapped to its corresponding -value with an arrow. This is a mapping that represents values from the function with the equation. Notice in the mapping of that the -values and both map to the -value. This sometimes happens with functions and is allowed as long as onl one arrow is drawn from each -value. If a mapping shows a single -value mapped to more than one -value (more than one arrow drawn from an -value), then the mapping is not a function. 7 Duplicating an part of this book is prohibited b law.

Lesson : Identifing Functions COACHED EXAMPLE Classif the relation shown b the mapping as a function or not a function. 8 THINKING IT THROUGH How man -values map to the -value? How man -values map to the -value? How man -values map to the -value? How man -values map to the -value? Do an of the -values map to more than one -value? Classif the relation as a function or not a function. Duplicating an part of this book is prohibited b law. 77

Lesson Practice Choose the correct answer.. Which relation is a function? A.. Which relation is not a function? A. 8 8 B. C. 7 9 8 7 7 8 7 B. 7 8 8 9 7 8 C. 8 8 D.. Which relation is a function? A. (, ), (, ), (, ), (, ) B. (, ), (, ), (, ), (, ) C. (, ), (9, 7), (, ), (9, 8) D. (, 7), (, ), (, 8), (, ) 7 7 7 D.. Which relation is not a function? A. (, ), (, ), (, 7), (8, 9) B. (, ), (, ), (, ), (, ) C. (, ), (, ), (, ), (, ) D. (, ), (7, ), (8, ), (8, 7) 78 Duplicating an part of this book is prohibited b law.

Lesson : Identifing Functions. Which graph shows a relation that is a function? A. B. C.. Which mapping shows a relation that is a function? A. B. C. D. 8 D. 7. Which relation is a function? A. (, ), (, ), (, ), (, ) B. (, 7), (, 8), (, 9), (, ) C. (, ), (, ), (, 8), (, 8) D. (, ), (, ), (, ), (, ) Duplicating an part of this book is prohibited b law. 79