ALGEBRA

1. RELATIONS
a set of ordered pairs

2. A relation can be represented by a set of
ordered pairs, a table, a graph, or a
mapping.

3. The DOMAIN (input) of a relation is the
x-coordinates of the ordered pairs.
The RANGE (output) of a relation is the
y-coordinates of the ordered pairs.

4. The INVERSE of a relation is found by
switching the coordinates of each
ordered pair.

5. FUNCTIONS
a relation when each element of the domain is
paired with exactly one element of the range.
• For every x there is exactly one y.
• The x-coordinate cannot repeat.

6. EXAMPLES THAT ARE FUNCTIONS:
EXAMPLES THAT ARE NOT FUNCTIONS:

7. VERTICAL LINE
TEST
test used to decide if a graph is a function.

8. EXAMPLE: FUNCTION!
If no vertical line can be drawn
so that it intersects the graph
more than once, then the
graph IS a function.

9. EXAMPLE: NOT A FUNCTION!
If any vertical line can be
drawn so that it intersects the
graph at two or more points,
then the relation IS NOT a
function.

10. FUNCTION
NOTATION
the y is replaced with f(x), read “f of x”

11. EVALUATING FUNCTIONS:

12. ANOTHER EXAMPLE:

13. THANK YOU!