SECTION 3.6 Function Notation and Linear Functions 193
NOW TRY
EXERCISE 6
Rewrite the equation using
function notation. Then
find and.
- 4 x^2 +y= 5
ƒ 1 - 32 ƒ 1 h 2ƒ 1 x 2Now find and
Letƒ 1 a 2 = Let x=a. NOW TRY
1
4
a-
5
4
ƒ 1 - 22 = x=-2.
1
4
1 - 22 -
5
4
=-
7
4
ƒ 1 - 22 ƒ 1 a 2.
Linear FunctionA function that can be defined by
for real numbers aand bis a linear function.The value of ais the slope mof the
graph of the function. The domain of any linear function is 1 - q, q 2.
ƒ 1 x 2 axb
OBJECTIVE 2 Graph linear and constant functions. Linear equations (except
for vertical lines with equations x= a) define linear functions.
A linear function whose graph is a horizontal line is defined by
and is sometimes called a constant function.While the range of any nonconstant lin-
ear function is 1 - q, q 2 ,the range of a constant function defined by ƒ 1 x 2 = bis 5 b 6.
ƒ 1 x 2 b
Graphing Linear and Constant FunctionsGraph each function. Give the domain and range.
(a) (from Example 6(b))
Slope y-intercept isThe graph of has slope and y-intercept To graph this
function, plot the y-intercept and use the definition of slope as to find a
second point on the line. Since the slope is move 1 unit up from and 4 units
to the right to find this second point. Draw the straight line through the points to
obtain the graph shown in FIGURE 50. The domain and range are both 1 - q, q 2.
A0, -^
54 B
14 ,
riseA0, -^ run
54 B
A0, -
5m= 4 B.
1y= 4
14 x-
5
4A0, -^54 B.ƒ 1 x 2 =
1
4
x-
5
4
EXAMPLE 7
NOW TRY ANSWERS
- ; ;
ƒ 1 h 2 = 4 h^2 + 5
ƒ 1 x 2 = 4 x^2 + 5 ƒ 1 - 32 = 41xy0f(x) =^14 x –^545- 4
1
m = 4
4–4–4FIGURE 50xy0f(x) = 42–4–2^24FIGURE 51(b)
The graph of this constant function is the horizontal line containing all points with
y-coordinate 4. See FIGURE 51. The domain is and the range is
NOW TRY1 - q, q 2 546.
ƒ 1 x 2 = 4
NOW TRY
EXERCISE 7
Graph the function. Give the
domain and range.
g 1 x 2 =1
3
x- 2domain: ;
range: 1 - q, q 21 - q, q 20y
x
(0, –2) (3, –1)2
6
f(x) =^13 x – 2Constant function