{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# Factoring gives us x 3x 1 0 so that x 3 or x 1

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: f the functions g , h, and i in Example 2.2.1 starting with the graph of f (x) = |x| and applying transformations as in Section 1.8. For example, the for the function g , we have g (x) = |x − 3| = f (x − 3). Theorem 1.3 tells us this causes the graph of f to be shifted to the right 3 units. Choosing three representative points on the graph of f , (−1, 1), (0, 0) and (1, 1), we can graph g as follows. y y 4 −3 −2 −1 3 2 (−1, 1) 4 3 2 (1, 1) 1 (0, 0) 1 2 f (x) = |x| 1 3 4 5 x shift right 3 unit −− − − − −→ −−−−−− add 3 to each x-coordinate −3 −2 −1 (2, 1) 1 (4, 1) 2 (3, 0) 4 5 x g (x) = f (x − 3) = |x − 3| Similarly, the graph of h in Example 2.2.1 can be understood via Theorem 1.2 as a vertical shift down 3 units. The function i can be graphed using Theorem 1.7 by ﬁnding the ﬁnal destinations of the three points (−1, 1), (0, 0) and (1, 1) and connecting them in the characteristic ‘∨’ fashion. While the methods in Section 1.8 can be used to graph an entire family of absolute value functions, not all functions involving absolute values posses the characteristic ‘∨’ shape, as the next example...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern