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Lesson 1.1 Essential Ideas A relation is a set of ordered pairs mapping between two sets, the domain and range. A relation is a set of ordered pairs mapping between two sets, the domain and range. The domain of a relation/function is the set of all possible input values. The domain of a relation/function is the set of all possible input values. The range of a relation/function is the set of all possible output values. The range of a relation/function is the set of all possible output values.

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A function is a relation that maps each member of the domain onto one and only one member of the range. A function is a relation that maps each member of the domain onto one and only one member of the range. Verbal descriptions, tables, diagrams, algebraic symbols, and graphs are used to represent relations and functions. Verbal descriptions, tables, diagrams, algebraic symbols, and graphs are used to represent relations and functions.

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Lesson 1.2 Essential Ideas The graph of a linear function is a line. The graph of a linear function is a line. The slope of a linear function is the unit rate of change and is constant. The slope of a linear function is the unit rate of change and is constant. The absolute value of a number is the distance from the number to zero on the number line. The absolute value of a number is the distance from the number to zero on the number line. The graph of an absolute value function is v-shaped, composed of two rays The graph of an absolute value function is v-shaped, composed of two rays

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An absolute value function has an extreme point (extrema) which is a minimum or maximum point, called a vertex. An absolute value function has an extreme point (extrema) which is a minimum or maximum point, called a vertex. When a line can be drawn on a graph that divides the graph into two mirror images, the graph has line symmetry. This line is called the line of symmetry. When a line can be drawn on a graph that divides the graph into two mirror images, the graph has line symmetry. This line is called the line of symmetry. The graph of an absolute function has a line of symmetry drawn through the vertex. The graph of an absolute function has a line of symmetry drawn through the vertex.

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Lesson 1.3 Essential Ideas Graphical representations provide us with information about the relationship between the independent and dependent variables, including increase, decrease, and no change. Graphical representations provide us with information about the relationship between the independent and dependent variables, including increase, decrease, and no change. An interval of increase is a set of values of x with no gaps for which y is increasing. An interval of decrease is a set of values of x with no gaps for which y is decreasing. An interval of increase is a set of values of x with no gaps for which y is increasing. An interval of decrease is a set of values of x with no gaps for which y is decreasing. A quadratic function is a function with an algebraic equation featuring an independent variable with an exponent of 2. A quadratic function is a function with an algebraic equation featuring an independent variable with an exponent of 2.

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The graph of a quadratic function is U-shaped. The graph of a quadratic function is U-shaped. The domain of a quadratic function is all numbers. The domain of a quadratic function is all numbers. The range of a quadratic function is all numbers greater than or equal to the y- value of the vertex, if the leading coefficient is positive, or all numbers less than or equal to the y-value of the vertex, if the leading coefficient is negative. The range of a quadratic function is all numbers greater than or equal to the y- value of the vertex, if the leading coefficient is positive, or all numbers less than or equal to the y-value of the vertex, if the leading coefficient is negative.

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The vertex of a quadratic function is the extreme point on the graph of the quadratic function. The vertex of a quadratic function is the extreme point on the graph of the quadratic function. The line of symmetry is the vertical line drawn through the vertex, with an equation of x = (the x-value of the vertex). The line of symmetry is the vertical line drawn through the vertex, with an equation of x = (the x-value of the vertex).

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Lesson 1.4 Essential Ideas A Cubic Function is a third-degree function A Cubic Function is a third-degree function An Indirect Variation Function is of the form y=k/x. An Indirect Variation Function is of the form y=k/x. In an indirect function, the values of the variables increase and decrease proportionally in opposite directions. In an indirect function, the values of the variables increase and decrease proportionally in opposite directions.

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Lesson 1.5 Essential Ideas A Square Root Function is a function in which the independent variable is under a radical symbol. A Square Root Function is a function in which the independent variable is under a radical symbol. An Exponential Function is a function in which the independent variable is an exponent. An Exponential Function is a function in which the independent variable is an exponent. The Average Rate of Change between two points on the graph of a function is the change in y divided by the change in x. The Average Rate of Change between two points on the graph of a function is the change in y divided by the change in x.

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