Stitz-Zeager_College_Algebra_e-book

# Product rule g uw g u g w in other words logb

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: h we have constructed are in order. As x → −∞ 1 Take a class in Diﬀerential Equations and you’ll see why. 330 Exponential and Logarithmic Functions and attains values like x = −100 or x = −1000, the function f (x) = 2x takes on values like 1 1 f (−100) = 2−100 = 2100 or f (−1000) = 2−1000 = 21000 . In other words, as x → −∞, 2x ≈ 1 ≈ very small (+) very big (+) So as x → −∞, 2x → 0+ . This is represented graphically using the x-axis (the line y = 0) as a horizontal asymptote. On the ﬂip side, as x → ∞, we ﬁnd f (100) = 2100 , f (1000) = 21000 , and so on, thus 2x → ∞. As a result, our graph suggests the range of f is (0, ∞). The graph of f passes the Horizontal Line Test which means f is one-to-one and hence invertible. We also note that when we ‘connected the dots in a pleasing fashion’, we have made the implicit assumption that f (x) = 2x is continuous2 and has a domain of all real numbers. In particular, we have suggested that things √ √ like 2 3 exist as real numbers. We should take a moment to discuss what something like 2 3 might mean, an...
View Full Document

## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online