SECTION 3.6 Introduction to Functions^233
CAUTION The notation does notmean ƒtimes x. It represents the y-value
that corresponds to x in function ƒ.
ƒ 1 x 2
Using Function NotationFor the function defined by find the following.
(a)
Let
Apply the exponent.
Subtract.(b)
(c)
= 6 NOW TRY
= 9 - 3
ƒ 1 - 32 = 1 - 322 - 3
=- 3
= 0 - 3
ƒ 102 = 02 - 3
= 13
= 16 - 3
ƒ 142 = 42 - 3 x=4.
ƒ 1 x 2 =x^2 - 3
ƒ 142
ƒ 1 x 2 = x^2 - 3,
EXAMPLE 5
OBJECTIVE 5 Use function notation.The letters ƒ, g, and hare commonly
used to name functions. The function ƒ defined by may be written
where , which represents the value of ƒat x, is read “ƒof x.”The notation
is another way of writing y in the function ƒ. For the function defined by
if then
Let
Multiply.
Add.Read this result, as “ƒof 7 equals 26.” The notation means the value
of ywhen xis 7. The statement says that the value of yis 26 when xis 7.
It also indicates that the point lies on the graph of ƒ.
Similarly, to find substitute for x.
LetMultiply.=- 4 Add.
=- 9 + 5
ƒ 1 - 32 = 31 - 32 + 5 x=-3.
ƒ 1 - 32 , - 3
1 7, 26 2
ƒ 172 = 26
ƒ 172 =26, ƒ 172
=26.
= 21 + 5
ƒ 172 = 3 # 7 + 5 x=7.
ƒ 1 x 2 = 3 x+5, x= 7,
ƒ 1 x 2 ƒ 1 x 2
ƒ 1 x 2 = 3 x+ 5,
y= 3 x+ 5
Use parentheses
to avoid errors.Function NotationIn the notation
ƒ is the name of the function,
x is the domain value,
and ƒ 1 x 2 is the range value yfor the domain value x.
ƒ 1 x 2 ,
NOW TRY
EXERCISE 5
Find for the function.
ƒ 1 x 2 =x^3 - 7ƒ 1 - 22Think: 4^2 = 4 # 4
Think: 1 - 322 =- 3 # 1 - 32
NOW TRY ANSWER
5.- 15