Unit+1

=Unit 1 Functions and Graphs=

=Video/Resources= []

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**Objectives**
You will understand how mathematics can model real-world behavior numerically, algebraically, and graphically. You will see how different kinds of models illustrate different aspects of that behavior, and you will begin to learn how to translate from one model to another. You will learn a general strategy for problem-solving based on the Polya four-step method. You will understand the problems of grapher failure and hidden behavior and know the difference between exploration and proof.
 * Key Ideas**
 * Algebraic model || Mathematical proof ||
 * Confirm (algebraically) || Numerical model ||
 * Grapher failure || Solve (numerically, graphically, algebraically) ||
 * Graphical model || Support (graphically, numerically) ||
 * Hidden behavior || Zero Factor property ||

**Objectives**
You will be able to represent functions numerically, algebraically, and graphically. You will be able to determine domains and ranges and analyze function characteristics such as extreme values, boundedness, asymptotes, symmetry, continuity, and end behavior. ==
 * Key Ideas**
 * Absolute maximum || Implied domain ||
 * Absolute minimum || Increasing on an interval ||
 * Bounded || Independent variable ||
 * Bounded above || Infinite discontinuity ||
 * Bounded below || Jump discontinuity ||
 * Constant on an interval || Local maximum ||
 * Continuity at a point || Local minimum ||
 * Decreasing on an interval || Mapping ||
 * Dependent variable || Odd function ||
 * Domain || Range ||
 * End behavior || Relevant domain ||
 * Even function || Removable disconinuity ||
 * Function || Symmetry ||
 * Horizontal asymptote || Vertical asymptote ||

**Objectives**
You will be able to use the vocabulary learned in Section 1.2 to analyze ten basic functions that appear on your calculator.
 * Key Ideas**

Basic Functions Piecewise-defined function

piecewise functions []

**Objectives**
You will be able to build functions from functions in several ways: by adding, subtracting, multiplying, or dividing functions, by composing functions, by defining functions parametrically, and by finding function inverses. You will be able to build up functions by composition and decompose functions into their basic components.
 * Key Ideas**
 * Function algebra (addition, multiplication, etc.) || Inverse function (or relation) ||
 * Function composition || Inverse reflection principle ||
 * Horizontal line test || Parameter ||
 * Implicitly defined function || Parametrically defined relation ||
 * Inverse composition rule || Relation ||

**Objectives**
You will be able to represent algebraically and graphically the basic transformations of functions: translations, reflections, stretches, and shrinks.
 * Key Ideas**
 * Reflection || Stretch (horizontal, vertical) ||
 * Rigid (or non-rigid) transformation || Transformation ||
 * Shrink (horizontal, vertical) || Translation (horizontal, vertical) ||

**Objectives**
You will be able to identify appropriate basic functions with which to model real-world problems. They will be able to produce specific functions to model data, formulas, graphs, and verbal descriptions.
 * Key Ideas**
 * Coefficient of determination || Correlation coefficient ||
 * Conversion factor || Regression line ||