SECTION 3.6 Function Notation and Linear Functions 191
NOW TRY
EXERCISE 2
Let.
Find the following.
(a)ƒ 1 - 22 (b)ƒ 1 a 2
ƒ 1 x 2 = 2 x^2 - 4 x+ 1(b)
Replace xwith q.The replacement of one variable with another is important in later courses.
NOW TRYƒ 1 q 2 =-q^2 + 5 q- 3
ƒ 1 x 2 =-x^2 + 5 x- 3
ƒ 1 q 2
Evaluating a FunctionLet Find and simplify.
Replace xwith.
Distributive propertyg 1 a+ 12 = 2 a+ 5 Add. NOW TRY
g 1 a+ 12 = 2 a+ 2 + 3
g 1 a+ 12 = 21 a+ 12 + 3 a+ 1
g 1 x 2 = 2 x+ 3
g 1 x 2 = 2 x+3. g 1 a+ 12
EXAMPLE 3
Evaluating FunctionsFor each function, find
(a) (b)
Replace xwith 3.
Multiply.ƒ 132 = 2 Subtract.
ƒ 132 = 9 - 7
ƒ 132 = 3132 - 7
ƒ 1 x 2 = 3 x- 7
ƒ 132.
EXAMPLE 4
–2
3
106
5
12f
Domain RangeNOW TRY
EXERCISE 3
Let. Find and
simplify .g 1 a- 22
g 1 x 2 = 8 x- 5NOW TRY
EXERCISE 4
Find for each function.
(a)
(b)ƒ 1 x 2 =x^2 - 12
1 - 1, 4 26
ƒ= 51 - 5, - 12 , 1 - 3, 2 2 ,ƒ 1 - 12NOW TRY ANSWERS
- (a) 17 (b)
- (a) 4 (b) - 11
8 a- 212 a^2 - 4 a+ 1Evaluating a FunctionLet Find the following.
(a)
The base in is x, not.
Replace xwith 4.
Apply the exponent. Multiply.
Add and subtract.Thus, ƒ 142 = 1,and the ordered pair 1 4, 1 2 belongs to ƒ.
ƒ 142 = 1
ƒ 142 =- 16 + 20 - 3
ƒ 142 =- 42 + 5 # 4 - 3
ƒ 1 x 2 =-x^2 + 5 x- 3 - x^21 - x 2
ƒ 142
ƒ 1 x 2 =-x^2 + 5 x-3.
EXAMPLE 2
Sometimes letters other than ƒ, such as g, h, or capital letters F, G, and Hare
used to name functions.
x
6
3
00- 3 6
- 6
- 12
y=ƒ 1 x 2(c)
We want the y-value of the ordered pair whose first component is
As indicated by the ordered pair 13 , 12 ,for x= 3,y= 1. Thus, ƒ 132 = 1.
ƒ 132 , x= 3.
ƒ= 51 - 3, 5 2 , 1 0, 3 2 , 1 3, 1 2 , 1 6, - 126
(d)
The domain element 3 is paired with 5 in the range, so
NOW TRYƒ 132 = 5.
Do notread this as
“ƒ times 4.” Read it as
“ƒ of 4.”Here, ƒ 132 =- 6.