4a)+Introduction+to+functions,+Domain+and+Range,+tests+for+a+function+(Section+2.1)

=**Unit 4: Linear Equations and Introduction to Functions:**= =**4a) Introduction to functions, Domain and Range, tests for a function (Section 2.1)**=

http://www.purplemath.com/modules/fcns2.htm
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A **function** connects each input to exactly one output


 * Domain** (input) of a relation is **THE SET OF ALL INPUTS** (x coordinates)
 * Range** (output) of a relation is **THE SET OF ALL OUTPUTS** (y coordinates)

f(5)
 * 1. Given function - f(x) = 3x +2- find the following**:

f(x) = 3x + 2 f(5) = 3(5) + 2 f(5) = 15 + 2 f(5) = 17
 * Answer**:

f(x) = -2x + 2
 * 2. Provide the domain and range of the following relation:**

Domain**: (negative infinity, infinity)
 * Answer:
 * Range**: (negative infinity, infinity)

{(-2,3)(1,2)(3,-1)(-4,-3)}
 * 3. Provide the domain and range of the following relation:**

**Answer:** Domain: {-4,-2,1,3} Range: {-3,-1,2,3}


 * 4. Is the above relation a function? Why?**

Yes, the relation is a function. Each input (each domain value) has exactly one output (range value). If an input were to have more than one output, the relation would not be a function.
 *  Answer: **

You could also use the "verticle line test" to check if something is a function. The verticle line test says "a relation is a function if and only if no vertical line intersects the graph of the relation at more than one point." (page 73)