9/15/10 (Chapter 1.1: Functions)

Chapter 1.1 - Functions:
... know that f(x) = y

• A function is a relation that assigns exactly one value in the domain to each value in the range. This means that for every x-value, there is only one y-value.

• The domain is...
  - the x-values
  - the input
  - the independent variable
• The range is...
  - the y-values
  - the output
  - the dependent variable
  
  
  

How to tell if an equation or a graph is a function:

• conduct a vertical line test...
  --> if the vertical line only intersects the graphed equation in one spot, it is a function.
  
  
  
  
  --> if the vertical line intersects the graphed equation multiple times, it is not considered a function.

• solve for y...
  • this is a function, the graphing of this equation will result in a parabola opening upwards.
    .
    
    
  • this is not a function, the graphing of this equation will result in a parabola opening to the right. (this would not pass the vertical line test)
    
    

!!! Indications that an equation might not be a function:

• if the y-value is in an absolute value (there would be two y-values for one x)
• if the y-value has a power greater than 1.