f(x) = [2x] = the greatest integer :£ 2x.
The domain consists of all real numbers. The range is the set of all integers. The graph (Fig. 5-6) is the
graph of a step function, with each step of length | and height 1.
Fig. 5-6
Fig. 5-7
g(jc) = [x/3] (see Problem 5.6).
The domain is the set of all real numbers and the range is the set of all integers. The graph (Fig. 5-7) is the
graph of a step function with each step of length 3 and height 1.
The domain is the set of all nonzero real numbers, and the range is the same set. The graph (Fig. 5-8) is the
hyperbola xy = 1.
Fig. 5-8
Fig. 5-9
5.10
The domain is the set of all real numbers ^ 1. The graph (Fig. 5-9) is Fig. 5-8 shifted one unit to the right.
The range consists of all nonzero real numbers.
The domain is the set of all real numbers, and the range is the same set. See Fig. 5-10.
Fig. 5-10
Fig. 5-11
The domain and range are the set of all real numbers. The graph (Fig. 5-11) is obtained by reflecting in the
jc-axis that part of the parabola y = x
2
that lies to the right of the >>-axis.
CHAPTER 5
5.6
24
5.7
5.8
5.9
5.11
J(x)=-x\x\.