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Function Notation
Traditionally, functions are referred
to by the letter name f, but f need not
be the only letter used in function
names. The following are but a few
of the notations that may be used to
name a function:
f (x), g(x), h(a), A(t), ...
Examples
f ( x)  x
g ( x)  3x  5
2
h( x)  1200(.5)
x
We mean the
same!
y  x 7
2
f ( x)  x  7
2
Evaluating Functions
To evaluate a function, simply replace
(substitute) the function's variable with the
indicated number or expression.
Examples
A function is represented by f (x) = 2x + 5.
Find f (3).
f (3) = 2(3) + 5 = 11
Find the value of
when m= - 2
g (m)  m  3m  11
3
2
g (2)  (2)  3(2)  11
3
g (2)  15
2
A function is represented f (x) = -2x + 4.
Find f (x + 6).
f ( x  6)  2( x  6)  4
 2 x  12  4
 2 x  8
a) Evaluate f(-3)
b) Evaluate f(0)
f(x)
Find the Domain and Range
Graphically
y  3x  1
y  x2 4
y  x  6x  4
2
1
y
x 1
y  x 1
1
y
x 1
Work on Evaluating Functions with a Partner
What did you notice about the domain?
y  3x  1
D: all Real #’s
1
y
x 1
D:{x | x  1}
y  x 1
y  x2 4
D: all Real #’s
D: {x | x  1}
y
y  x2  6x  4
D: all Real #’s
1
x 1
D:{x | x  1}
Restricted Domains
The domain is all real numbers except when
there is a…
• Case 1: Variable in the Denominator
– Set the denominator ≠ 0 and solve
– Example:
3
• Find the Domain of y 
x4
x4 0
x4
Restricted Domains
• Case 2: Variable under Square Root
– Set the radicand ≥ 0 and solve
– Example: Find the Domain of
y  x7
x7  0
x7
Restricted Domains
• Case 3: Variable under Square Root AND in
the denominator
– Set the radicand in the denominator > 0 and solve
3
– Example: Find the domain of y 
x6
x60
x  6
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