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Domain and Range By Kaitlyn, Cori, and Thaiz

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Domain Most commonly used definition- The set of all possible values "X" can have in a particular given equation. The domain can be written in bracket form or can be simply written out. Examples: Bracket form: (-3,5) or [10,45] {sometimes can be a combination of the two, refer to bracket slide} ; Written out: The domain begins at -3 and continue to and includes 5.

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Range Most Commonly used definition- The set of all possible values "Y" can have in a particular given equation. The Range can also be written in Bracket form and can be written out. Example: Bracket form: (-inf., 25] ; Written out form: the graph ranges from negative infinity and stop at but includes 25.

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The rules of brackets When the end numbers are included in a specific situation or graph, when writing in bracket form you must use hard brackets [] When the end numbers are not included in a situation or graph, when writing in bracket form you must use soft brackets () In some cases you can use soft and hard brackets in the same Domain/Range -inf. and inf. are always put in soft brackets

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Linear equations In linear equations such as: 3x+4, The domain and range will always be (-inf.,inf.) Because the shape of the graph is obviously always a simple line. In some situations, you may need to restrict the domain and range and in these cases you will most likely need to use hard brackets.

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Quadratics In Quadratic equations such as x^2+4x+8, the graph is always in the shape of a "U" or upside- down "U". In this situation, the domain is always (-inf.,inf.) while the range is a restricted number (the vertex) and then either inf. (if the graph is positive) or -inf. (if the graph is negative).

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Even Radicals Even radicals are square roots, the 4th root of x and so on. The domain of an even radical is the x value of its vertex in a hard bracket to inf in a soft bracket. The range of an even radical is its y value of its vertex in hard brackets to inf in soft brackets Example: if the vertex of an even radical is (3,5); its domain is [3,inf) and its range is [5,inf)

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Odd Radicals Odd radicals are cubed roots, the 5th root of x and so on. The domain for odd radicals is (-inf,inf) The range for odd radicals is (-inf,inf)

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Absolute Values Even absolute values always have a domain of (inf,inf) Odd absolute values always have a domain of (-inf,- inf) The range of an even absolute values is the y value of its vertex in hard brackets and inf in soft brackets The range of odd absolute values are the y values of the vertex in hard brackets and -inf in soft brackets Examples: if the vertex of and even absolute value is (3,4) the range is [4,inf). if the vertex of an odd absolute value is (1,6) the range is [6,-inf)

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The line is never ending, which means the domain and range are all real numbers. The equation of the graph is y=-2x+3. The domain and range is x (-inf., inf.), y(-inf., inf.) Linear Equation Domain and Range

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The equation for this graph is f(x)=x^9-2x^2+3. The function is never ending, so the domain and range is x (-inf., inf.) y (- inf.,inf.). The range of every odd powered polynomial function is (-inf., inf.) Polynomial Equation Domain and Range

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Domain and Range Domain is the possible inputs values on the X axis that allows a function to work. Range is the possible outputs on the Y axis as a result of the function. Both domain and range can be written in bracket form. There are two types of brackets, open (), and closed [] brackets. Domain and range are written to show the possible inputs and outputs of both linear and polynomial equations.

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Aim: What is the complex number? Do Now: Solve for x: 1. x 2 – 1 = 0 2. x 2 + 1 = 0 3. (x + 1) 2 = – 4 Homework: p.208 # 6,8,12,14,16,44,46,50.

Aim: What is the complex number? Do Now: Solve for x: 1. x 2 – 1 = 0 2. x 2 + 1 = 0 3. (x + 1) 2 = – 4 Homework: p.208 # 6,8,12,14,16,44,46,50.

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