College Algebra 9th txtbk

SECTION 3–2 Graphing Functions 177
f(x)
f(x)
d
[ ]
a
[ ]
b
c
x
(
a
d
(
x
Domain f [a, b]
Range f [c, d]
Domain f (a, )
Range f (, d)
(a)
(b)
Z Figure 2 Domain and range.
EXAMPLE 2 Finding the Domain and Range from a Graph
(A) Find the domain and range of the function f whose graph is shown in Figure 3.
(B) Find f(1), f(3), and f(5).
y or f(x)
4
3
1
3 5
x
y f(x)
4
5
Z Figure 3
SOLUTIONS
y or f(x)
3
1
4
y f(x)
5
x
4
Z Figure 4
(A) The dot at the left end of the graph indicates that the graph terminates at that point,
while the arrowhead on the right end indicates that the graph continues infinitely far
to the right. So the x coordinates on the graph go from 3 to . The open dot at
(3, 4) indicates that 3 is not in the domain of f.
Domain: 3 6 x 6 or (3, )
The least y coordinate on the graph is 5, and there is no greatest y coordinate.
(The arrowhead tells us that the graph continues infinitely far upward.) The closed
dot at (3, 5) indicates that 5 is in the range of f.
Range: 5 y 6 or [ 5, )
(B) The point on the graph with x coordinate 1 is (1, 4), so f(1) 4. Likewise,
(3, 5) and (5, 4) are on the graph, so f(3) 5 and f(5) 4.
MATCHED PROBLEM 2 (A) Find the domain and range of the function f given by the graph in Figure 4.
(B) Find f(–4), f(0), and f(2).
ZZZ CAUTION ZZZ
When using interval notation to describe domain and range, make sure that you always
write the least number first! You should find the domain by working left to right along
the x axis, and find the range by working bottom to top along the y axis.