College Algebra, 2013a

6.1 Introduction to Exponential and Logarithmic Functions 419
note that g(x) = ( 1
2) x =
(
2
−1 ) x =2 −x = f(−x), where f(x) =2 x . Thinking back to Section 1.7,
the graph of f(−x) is obtained from the graph of f(x) by reflecting it across the y-axis. We get
8
7
6
5
4
3
2
1
y
−3−2−1 1 2 3
y = f(x) =2 x
x
reflect across y-axis
−−−−−−−−−−−−→
multiply each x-coordinate by −1
8
7
6
5
4
3
2
1
−3−2−1 1 2 3 x
y = g(x) =2 −x = ( ) 1 x
2
We see that the domain and range of g match that of f, namely(−∞, ∞) and(0, ∞), respectively.
Like f, g is also one-to-one. Whereas f is always increasing, g is always decreasing. As a result,
as x →−∞, g(x) →∞, and on the flip side, as x →∞, g(x) → 0 + . It shouldn’t be too surprising
that for all choices of the base 0