6. Vocabulary
• Function: A special type of Relation in which
each input value (Domain) is matchup up
with exactly one output value (Range).
Usually we describe a function with an equation.
9. Vocabulary
• Function: Rule that assigns each input value
to exactly one output.
Usually we describe a function with an equation.
• Domain: x –values, or input values.
• Range: y – values , or output values.
10. How do we know if a graph is a
function?
• If it passes THE VERTICAL LINE TEST
The vertical line test
1. Move a vertical line across the entire graph
from left to right.
2. If it intersects the graph only ONCE in all
locations, then it is a function.
18. Practice
1. Is a function represented? If so what is the
domain and range.
a. (2,-4) (4,4) (6,-1) (5,0) (1,6) (2,4) (3, -2)
b.
2. If , then find f (0) , f (-2) , and f (3a)5)( 2
xxf
19. Finding the domain from the equation
Example: What is the domain of the function given
by
Functions only have real number outputs.
Anything that gives an imaginary number or a
zero denominator is a restriction.
How to find the domain:
Assume that the domain is the set of all real
numbers except for the restrictions.
5)( xxf
20. Examples
• What is the domain?
• What is the domain?
7
2
)(
x
xf
9
7
)( 2
x
xf
