Stitz-Zeager_College_Algebra_e-book

There is no such real number since all powers of 2

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: h x the graph of k passes the Horizontal Line Test which means k is one to one and k −1 exists. Computing k −1 is left as an exercise. (−) −1 (+) 1 y = k (x) As the previous example illustrates, the graphs of general algebraic functions can have features we’ve seen before, like vertical and horizontal asymptotes, but they can occur in new and exciting 2x ways. For example, k (x) = √x2 −1 had two distinct horizontal asymptotes. You’ll recall that rational functions could have at most one horizontal asymptote. Also some new characteristics like ‘unusual steepness’8 and cusps9 can appear in the graphs of arbitrary algebraic functions. Our next example first demonstrates how we can use sign diagrams to solve nonlinear inequalities. (Don’t panic. The technique is very similar to the ones used in Chapters 2, 3 and 4.) We then check our answers graphically with a calculator and see some of the new graphical features of the functions in this extended family. Example 5.3.2. Solve the following inequalities. Check you...
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