## Topic outline

### General

### Unit 1

In this unit we will learn how to graph inequalities in one and two variables and explore the region on the graph that represents the solutions to the inequality. We will learn to solve systems of two or more inequalities by graphing and locating the region on the graph that represents the solutions all the inequalities have in common. We will apply our work with systems of linear inequalities to solve linear programming problems that involve maximizing or minimizing an outcome.

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Students: Use these pages as a resource guide for an explanation of all the work contained within the unit. For each unit have the Reference and Resource guide out to explain how to do the classwork, work through the classwork and then check your answers. When you have completed the classwork you may begin the corresponding practice problem sections. Once complete check your practice problem answers.

Identified Learning Targets:

1.1 I can demonstrate understanding of how to represent a region on a graph with an inequality.

1.2 I can demonstrate understanding of real-world situations that can be modeled as linear equations or linear inequalities.

1.3 I can represent real-world situations as a linear programming problem and demonstrate

an understanding of how to find reasonable solutions.

Student Class Work and Practice

### Unit 2 Functions

The concept of function may be the single most important concept spanning all branches of mathematics. We will learn how to recognize when a relationship is a function and to evaluate a function for a given input. We will work with functions represented in various ways. We will recognize and interpret key features of functions represented with graphs, tables, and equations. We will relate these features to what is occurring in mathematical and real world situations. The key features include: intercepts; intervals where the function is increasing or decreasing; when the value of the function is positive or negative; relative maximums and minimums; symmetries; domain (input) and range (output); inverse relationships; and rate of change.

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Students: Use these pages as a resource guide for an explanation of all the work contained within the unit. For each unit have the Reference and Resource guide out to explain how to do the classwork, work through the classwork and then check your answers. When you have completed the classwork you may begin the corresponding practice problem sections. Once complete check your practice problem answers.

Identified Learning Targets:

2.1 I can demonstrate understanding of the definition of a function and can determine when relations are functions given a graph, table or real-world situation.

2.2 I understand the meaning of function notation and can evaluate a function for a given input.

2.3 I can demonstrate understanding of the significant features of a function represented by

a graph, a table, or an equation and the relationship these features have to real-world

situations.

Student Class and Practice Work

### Unit 3 Exponential Functions

Exponential functions occur frequently in real world situations. They are used to model the growth of human and animal populations, chemical processes such as radioactive decay, and financial applications such as the compound growth of the value of an investment. Students learn about exponential functions by comparing the situations and equations for exponential functions to those for linear functions. Students recognize, use, and create tables, graphs and situations modeling exponential growth and decay. Students are able to evaluate exponential functions with rational number inputs and to relate the meaning of a rational exponent to the context of the situation. Students use tables and graphs to solve exponential equations and translate between representations.

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Students: Use these pages as a resource guide for an explanation of all the work contained within the unit. For each unit have the Reference and Resource guide out to explain how to do the classwork, work through the classwork and then check your answers. When you have completed the classwork you may begin the corresponding practice problem sections. Once complete check your practice problem answers.

Identified Learning Targets:

3.1 I can demonstrate understanding about exponential functions and compare situations and equations for exponential functions to those for linear functions.

3.2 I can use tables and graphs to solve exponential equations including real world situations and translate between representations.

3.3 I can evaluate exponential functions in the form y = a·b real-world situation.

3.4 I can demonstrate understanding of the significant features of a graph of an exponential function and their relationship to real-world situations.

Student Class and Practice Work

### Unit 4 Modeling with Quadratic Functions

Students use various forms of quadratic equations to graph parabolas with a focus on using the line of symmetry and the vertex. Though students will be working on converting between different forms of equations for parabolas (multiplying binomials, completing the square, and factoring), the focus is on extending their understanding from Unit 2 and recognizing the advantages of determining the location of the vertex when graphing a parabola. Students analyze graphs of quadratic functions, use graphs and tables to solve real-world situations, and translate between representations.

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Identified Learning Targets:

4.1 I can graph quadratic functions and demonstrate understanding of significant features of

different forms of quadratic equations and their real-world situations.

4.2 I can translate quadratic equations from factored and vertex forms into standard form.

4.3 I can translate quadratic equations from standard form into factored and vertex forms.

different forms of quadratic equations and their real-world situations.

Student Class Work

### Unit 5 Solving Quadratic Equations

Students solve quadratic equations by factoring, finding square roots, completing the square, and by using the quadratic formula. Students determine the number of rational, real, and non-real solutions by factoring or solving the equation and also by using the graph. Students understand that the quadratic formula can be found by completing the square and use the symmetry in the graph of a parabola to identify how the x-coordinate for the vertex can be seen in the quadratic formula.

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Identified Learning Targets:

5.1 I can use tables and graphs to solve quadratic equations including real-world situations and translate between representations.

5.2 I can represent real-world situations with quadratic equations and solve using appropriate methods. Find real and non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context.

5.3 I can determine the number of real and non-real solutions for a quadratic equation.

5.4 I can represent relationships involving quadratic inequalities in multiple ways, find solutions and interpret these solutions to solve real-world situations.

Embedded throughout the unit:

• I understand how to verify that an answer is a solution and can interpret the solution.

• I can demonstrate understanding of the real and non-real number systems and mathematical context of the situation.

• I can demonstrate understanding of the real and non-real number systems and mathematical operations using expressions from these number systems.

### Unit 6 Polynomial Functions

Students extend earlier work with expressions to adding, subtracting, and multiplying polynomials. Students graph real-world situations that can be modeled with polynomial functions and analyze the graphs of polynomial functions. Students solve polynomial equations graphically, by using tables or by finding rational roots algebraically. Students will translate between representations of polynomial functions.

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Identified Learning Targets:

6.1 I can graph polynomial functions and demonstrate understanding of the significant

features of its graph and their relationship to real-world situations.

6.2 I can demonstrate understanding of operations with polynomials.

6.3 I can demonstrate understanding of how to solve polynomial equations.

### Unit 7 Root Functions and Radical Equations

Students graph square root functions and analyze the graph to identify its key features. Students evaluate and simplify radical expressions. Students solve equations with radical expressions and identify possible extraneous solutions. Students translate between representations.

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Identified Learning Targets:

7.1 I can graph square root and cube root functions and demonstrate understanding of the significant features of its graph.

7.2 I can demonstrate understanding of radical expressions and expressions with rational exponents.

7.3 I can solve equations with radical expressions and expressions with rational exponents.

### Unit 8 Absolute Value Functions

Students graph real-world situations that can be modeled with absolute value functions and analyze the graphs of absolute value functions. Students solve absolute value equations and inequalities involving linear expressions in two variables by graphing, using tables and solving related equations. Students translate between representations.

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Identified Learning Targets:

8.1 I can graph absolute value equations and inequalities and demonstrate understanding of the

significant features of its graph.

8.2 I can find solutions of absolute value equations and inequalities.