Stitz-Zeager_College_Algebra_e-book

We conrm the domain of g is 0 and nd the range of g

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: t to the reader to verify that the domain of j is the same as f , but the range of j is [−1, 3]. What we have discussed is generalized in the following theorem. Theorem 1.2. Vertical Shifts. Suppose f is a function and k is a positive number. • To graph y = f (x) + k , shift the graph of y = f (x) up k units by adding k to the y -coordinates of the points on the graph of f . • To graph y = f (x) − k , shift the graph of y = f (x) down k units by subtracting k from the y -coordinates of the points on the graph of f . The key to understanding Theorem 1.2 and, indeed, all of the theorems in this section comes from an understanding of the Fundamental Graphing Principle for Functions. If (a, b) is on the graph of f , then f (a) = b. Substituting x = a into the equation y = f (x) + k gives y = f (a) + k = b + k . Hence, (a, b + k ) is on the graph of y = f (x) + k , and we have the result. In the language of ‘inputs’ and ‘outputs’, Theorem 1.2 can be paraphrased as “Adding to, or subtracting...
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