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Algebra I
GN Relations, Functions and Classifying
Do Now: Circle each of the categories that each number is a member of
Circle the categories that each of the following numbers are members of.
1.
10
real
rational
irrational
integer
whole
natural
2. 8.2
real
rational
irrational
integer
whole
natural
3. 4.43
real
rational
irrational
integer
whole
natural
4.
64
real
rational
irrational
integer
whole
natural
5. -
21
35
real
rational
irrational
integer
whole
natural
real
rational
irrational
integer
whole
natural
real
rational
irrational
integer
whole
natural
6.
7.
p
50
Relations and Functions
-
What is a relation? ________________________________________________
-
What is a function? _________________________________________________
_______________________________________________________________________
**Functions are usually written a few different ways:
-
Domain : _________________________________________________________
- Range: ___________________________________________________________
- Inverse: _________________________________________________________
1.)
Use the relation to draw a graph, table, and mapping. Identify the domain, range, and inverse of the
relation.
{(0, 4), (-4, -4), (-2, 3), (4, 0)}
X
Y
X
Y
Domain: { _________ }
Range:
{ _________ }
Inverse: { ________________________ }
2.) Determine whether each relation is a function.
a.
d.
b.
c.
{(1, 4), (2, -2), (3, -6), (-6, 3), (-3, 6)}
3.) If f(x) = 2x – 6 and g(x) = x – 2x2, find each value.
a.
c.
f(
)
f(a + 5)
b.
g(-5)
d.
g(3y)
Composition of Functions: __________________________________________________________
______________________________________________________________________________
***When doing a composition, always work from the inside out***
EX:
If f(x) = 2x – 6 and g(x) = x – 2x2, find each value
a.
f(g(1))
b.
g(f(4))
c.
f(f(2))
d.
g(g(-4))
e.
f(g(f(2)))
f.
f(g(x))
Identify the domain and range in the graphs below.
1.
2.
Domain: ____________
Domain: ____________
Range: ____________
Range: ____________
3.
4.
Domain: ____________
Domain: ____________
Range: ____________
Range: ____________
5.
6.
7.
Domain: ____________
Domain: ____________
Domain: ____________
Range: ____________
Range: ____________
Range: ____________