Unformatted text preview: o be r is (−∞, 1) ∪ (1, ∞). Setting r(x) = 0 gives x = 0. (+) 0 (−)
0
8 See page 44 if you’ve forgotten what this term means. (+)
1 338 Exponential and Logarithmic Functions
x
We ﬁnd x−1 > 0 on (−∞, 0) ∪ (1, ∞) to get the domain of g . The graph of y = g (x) conﬁrms
this. We can tell from the graph of g that it is not the result of Section 1.8 transformations
being applied to the graph y = ln(x), so barring a more detailed analysis using Calculus, the
calculator graph is the best we can do. One thing worthy of note, however, is the end behavior
of g . The graph suggests that as x → ±∞, g (x) → 0. We can verify this analytically. Using
x
results from Chapter 4 and continuity, we know that as x → ±∞, x−1 ≈ 1. Hence, it makes sense that g (x) = ln x
x−1 ≈ ln(1) = 0. y = f (x) = 2 log(3 − x) − 1 y = g (x) = ln x
x−1 While logarithms have some interesting applications of their own which you’ll explore in the exercises, their primary use to us will be to undo exponential functions. (Thi...
View
Full Document
 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

Click to edit the document details