Unit 4: Linear Equations and Introduction to Functions:

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


For more information, visit:
http://www.purplemath.com/modules/fcns2.htm

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)



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

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

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

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

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

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


4. Is the above relation a function? Why?

Answer:
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.

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)