Domain and Range By Kaitlyn, Cori, and Thaiz

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.

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.

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

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.

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).

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)

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)

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)

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

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

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.