{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

# F is one to one continuous and smooth ba c if and only

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: ons are x = ±1, both of which must be excluded from the domain. Hence, the domain of k is (−∞, −1) ∪ (1, ∞). To 2x build the sign diagram for k , we need the zeros of k . Setting k (x) = 0 results in √x2 −1 = 0. We get 2x = 0 or x = 0. However, x = 0 isn’t in the domain of k , which means k has no zeros. We construct our sign diagram on the domain of k below alongside the graph of k . It appears that the graph of k has two vertical asymptotes, one at x = −1 and one at x = 1. The gap in the graph between the asymptotes is because of the gap in the domain of k . Concerning end behavior, there appear to be two horizontal asymptotes, y = 2 and y = −2. To see why this is the case, we think of x → ±∞. The radicand of the denominator x2 − 1 ≈ x2 , and as 2x 2 x x such, k (x) = √x2 −1 ≈ √ x2 = |2x| . As x → ∞, we have |x| = x so k (x) ≈ 2x = 2. On the other x 2 hand, as x → −∞, |x| = −x, and as such k (x) ≈ −x = −2. Finally, it appears as thoug...
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