College Algebra - Section 3.1 (Packet #1)
By the end of the section, you should be able to:
- Explain the following: relation, domain, and range.
- Be able to find the domain and/or range of a relation or function.
- Determine whether a relation is a function using the Vertical Line Test.
- Use function notation to evaluate functions.
- Find the implied domain of a function.
Definitions:
- Relation: a set of pairs of input and output values.
- Domain: the set of inputs (x-coordinates of an ordered pair)
- The set of the independent variables
- Range: the set of outputs (y-coordinates of an ordered pair)
- The set of the dependent variables
- Implied Domain: the domain of the function that is implied by the formula used in defining the function.
- It is assumed that the domain of the function consists of all those real numbers at which the function can be evaluated to obtain a real number.
- Function: a relation in which each element of the domain corresponds with exactly one element of the range.
- Vertical Line Test: if a vertical line passes through more than one point on the graph of the relation, then the relation is NOT a function.
- Function Rule: an equation that represents an output value in terms of an input value
- Function Notation: f(x) is used as the output rather than y
- y = f(x)
Four Ways to Represent Relations
A way to remember Domain vs. Range
Examples of parts of Relations and Functions
🎥Explained ** I made an Error in this video, for the first mapping diagram the orderd pairs should be (-3,-2) (0,7) and (4,1)**
**For more examples look at Algebra 2 – Section 2.1 Notes**
Examples of Finding Domain and Range of a Given Relation
Examples of Finding Domain and Range of a Given Relation
Function Notation
Implied Domain
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