basic concepts of Functions

1. FUNCTIONS : DOMAIN AND
RANGE

8. Domain: In a set of ordered
pairs, (x, y), the domain is
the set of all x-coordinates.
Range: In a set of ordered
pairs, (x, y), the range is the
set of all y-coordinates.

9. The set of ordered pairs may be a
limited number of points.
Given the following set of ordered pairs, find
the domain and range.
Ex:{(2,3),(-1,0),(2,-5),(0,-3)}
Domain: {2,-1,0}
Range: {3,0,-5,-3}
If a number occurs
more than once,
you do not need to
list it more than
one time.

10. The set of ordered pairs may be an
infinite number of points, described
by a graph.
6
5
Given the
following graph,
find the domain
and range.
4
3
2
1
-6
-4
-2
2
-1
4

11. 6
5
4
3
2
1
-6
-4
-2
2
4
-1
Domain:{all real numbers}
Range:{y:y≥0}
6

12. The set of ordered pairs may be an
infinite number of points, described
by an algebraic expression.
Given the following function, find the domain
and range.
Example: f (x) =
x−5
Domain: {x: x≥5}
Range: {y: y≥0}

13. Practice: Find the domain and
range of the following sets of
ordered pairs.
1. {(3,7),(-3,7),(7,-2),(-8,-5),(0,-1)}
Domain:{3,-3,7,-8,0}
Range:{7,-2,-5,-1}

14. 2.
10
5
-10
10
20
-5
-10
Domain={x:x ≥ 3} Range:{all reals}
-15

15. 3. f (x) = 3x − 4
Domain={all reals}
2
Range:{y:y≥-4}
2
4. f (x) =
x
Domain={x:x≠0}
Range:{y:y≠0}

16. 5. x + y = 4
Domain={x: -2≤x≤2}
2
2
Note: This is NOT a
Function!
Range:{y: -2≤y≤2}
6. f (x) = 3(x − 1) + 2
Domain={all reals}
Range:{all reals}