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.