Are Domain_3 And Wavelength Related

Domain and range

The domain and range of a function is all the possible values of the independent variable, 10, for which y is defined. The range of a part is all the possible values of the dependent variable y.

The case beneath shows two dissimilar ways that a part tin be represented: equally a function tabular array, and equally a prepare of coordinates.

x	y
ii	iv
three	8
5	2
half dozen	9
viii	iii

{(2, iv), (3, viii), (5,2), (6,nine), (8,three)}

Fifty-fifty though they are represented differently, the in a higher place are the aforementioned function, and the domain of the function is ten = {ii, iii, 5, half-dozen, 8} and the range is y = {iv, 8, ii, nine, 3}. This is how you can defined the domain and range for discrete functions. The gild in which you list the values does non thing. But how do you define the domain and range for functions that are not discrete?

Example:

f(x) = ten²

The function f(x) = tenⁱⁱ has a domain of all existent numbers (x can be anything) and a range that is greater than or equal to null.

Two ways in which the domain and range of a function can be written are: interval notation and set note.

Interval notation

When using interval notation, domain and range are written as intervals of values. For f(x) = x² , the domain in interval notation is:

D: (-∞, ∞)

D indicates that you are talking about the domain, and (-∞, ∞), read as negative infinity to positive infinity, is another fashion of saying that the domain is "all real numbers."

The range of f(x) = xⁱⁱ in interval annotation is:

R: [0, ∞)

R indicates that you are talking nearly the range. Notice that a bracket is used for the 0 instead of a parenthesis. This is because the range of a part includes 0 at x = 0. The range of the office excludes ∞ (every function does), which is why we use a round bracket.

On a graph, yous know when a part includes or excludes an endpoint considering the endpoint will be open or airtight.

Set notation

When using set notation, we apply inequality symbols to describe the domain and range every bit a set of values. The domains and ranges used in the discrete function examples were simplified versions of set notation. There are many different symbols used in set notation, but only the most basic of structures will be provided here.

The domain of f(x) = x² in prepare notation is:

D: {x | 10∈ℝ}

Again, D indicates domain. The "|" means "such that," the symbol ∈ means "element of," and "ℝ" means "all existent numbers."

Putting information technology all together, this argument tin can be read as "the domain is the set of all x such that x is an element of all real numbers."

The range of f(x) = xⁱⁱ in set notation is:

R: {y | y ≥ 0}

R indicates range. When using set notation, inequality symbols such as ≥ are used to describe the domain and range. Therefore, this statement tin can exist read every bit "the range is the set of all y such that y is greater than or equal to nix."