In the previous examples, we used inequalities and lists to describe the domain of functions. We can also use inequalities, or other statements that might define sets of values or data, to describe the behavior of the variable in set-builder notation. For example, \displaystyle \left\ {x|10\le x
Given a rational function, find the domain. 1. Set the denominator equal to zero. 2. Solve to find the -values that cause the denominator to equal zero. 3. The domain is all real numbers except those found in Step 2. EXAMPLE 4 Finding the Domain of a Rational Function. Find the domain of . Solution. Begin by setting the denominator equal to Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x x -axis. The range is the set of possible output values, which are shown on the y y -axis. Keep in mind that if the graph continues These will all pass the vertical line test. that will fit this equation; any real value squared will be a positive number. is defined for all real values of . This makes the domain of the set of all real numbers. Free practice questions for Algebra II - Domain and Range. Includes full solutions and score reporting.

Restricted Domain and Range. Set of all values of the independent inputs (x) or dependent outputs (y) variable of a function and interval notation. % Progress

Yet, we can still determine the domain and range of this relation. Recall, the domain is the set of all x-values. Here are the x-values in set H. Domain = {-2, -1, 0, 1, 2} Take care to notice that two '1's were not listed because it is unnecessary to duplicate domain values. Those five values are the only x-values that set H takes on. To

Cosine. θ = R. − 1 ≤ y ≤ 1. Knowing the domain and range of the cosine and sine function can help us determine the domain and range of the secant and cosecant function. First consider the sine and cosecant functions, which as we showed above, are reciprocals. The cosecant function will be defined as long as the sine value is not 0.
Ques. Determine the domain and range of y = 3 tan x. Solution: We are aware domain and range of trigonometric function tan x can be represented by, Domain = R - (2n + 1)π/2, Range = (-∞, +∞) The domain, in this case, is denoted by values x can carry, meaning that the domains of tan x and 3 tan x are similar.
Definition. A domain defines a value range. A domain is assigned to a data element. All table fields or structure components that use this data element have the value range defined by the domain. The relationship between the field or component and the domain is defined by the data element of the field or component. Use
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    • meaning of domain and range