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Here are some tips for Domain and Range, which aligns with Florida state standards:

Domain and Range

The domain of a function is the set of all possible input values. The range of a function is the set of all possible output values.
By definition of a function, each member in the domain maps to only one member in the range.
Function: Domain: y = x + 4 f(x) = x2 - 25x x x y f(x)

Here are examples of possible values for domains and ranges:
Notation Definition
{1, 3, 5} Only 1, 3, 5 are members
(-∞, ∞) All real numbers
(3, ∞) All real numbers greater than 3
[3, ∞) All real numbers greater than or equal to 3
(-∞, 0] All real numbers less than or equal to 0
(-∞, 2) ∪ (3, 10) All real numbers less than 2 AND all real numbers between 3 and 10

Note the difference in brackets { } ( ) [ ].

Example 1: Ordered Pairs

Find the domain and range. Give answers in ascending order. Example: {-2, 1, 5} but not {1, -2, 5}
{ (8, 13), (5, -2), (4, 11), (8, 12) }       Domain: Range:

The domain contains all the input values: 8, 5, 4, 8
The range contains all the output values: 13, -2, 11, 12

Remember that duplicate values only need to be listed once.

Example 2: Graphs

Find the domain and range. For ∞, use "inf". Example: Use (-inf, inf) for (-∞, ∞)
 Domain: Range:

The domain is all the possible x values and the range is all the possible y values.
From the graph, you can see that x can be all real numbers and y can only be 5.
So the answer is Domain: Range:

Example 3: Expressions

Find the domain and range. For ∞, use "inf". Example: Use (-inf, inf) for (-∞, ∞)
For the union symbol ∪, use capital "U".
 f(x) = √x - 1 Domain: Range:

Expressions under radicals must be greater or equal to 0.
To find the domain, solve x - 1 ≥ 0:
 x - 1 ≥ 0 x - 1 + 1 ≥ 0 + 1 x ≥ 1

To find the range, square roots must be greater or equal to 0. Therefore, f(x) ≥ 0.