College Algebra 9th txtbk

SECTION 3–2 Graphing Functions 183
Technology Connections
Most graphing calculators denote the greatest integer
function as int (x), although not all define it the same way
we have here. Graph y int (x) for 5 x 5 and
5 y 5 and discuss any differences between your
graph and Figure 7. If your graphing calculator supports
both a connected mode and a dot mode for graphing functions
(consult your manual), which mode is preferable for
this graph?
EXAMPLE 6 Computer Science
Let
Find:
f (x)
10x 0.5
10
(A) f(6) (B) f(1.8) (C) f(3.24) (D) f(4.582) (E) f(2.68)
What operation does this function perform?
60.5
SOLUTIONS (A) f (6) 60 (B) f (1.8) 18.5
Table 3
10 10 6
10
18
10 1.8
x
f(x)
32.9
(C) f (3.24) 32 (D) f (4.582) 46.32 46
10 10 3.2 10 10 4.6
6 6
(E) f (2.68) 26.3 27
1.8 1.8
10 10 2.7
3.24 3.2
Comparing the values of x and f(x) in Table 3 in the margin, we conclude that this function
4.582 4.6
rounds decimal fractions to the nearest tenth. The greatest integer function is used in
2.68 2.7
programming (spreadsheets, for example) to round numbers to a specified accuracy.
MATCHED PROBLEM 6
Let f(x) x 0.5. Find:
(A) f(6) (B) f(1.8) (C) f(3.24) (D) f(4.3) (E) f(2.69)
What operation does this function perform?
ANSWERS TO MATCHED PROBLEMS
1. Domain: (, 2 3) ( 2 3, ) ; x intercept: 5 4; y intercept: f (0) 5 2
2. (A) Domain: (4, 5); range: (4, 3] (B) f (4) 1, f (0) 3, f (2) 2
3. y intercept: f(0) 6
y
x intercept: 4
Slope: 3 2
x
5
5