3.5_bzca5e - Section 3.5 Rational Functions and Their...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 3.5 Rational Functions and Their Graphs
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Rational Functions
Image of page 2
Rational Functions are quotients of polynomial functions. This means that rational functions can ( ) be expressed as f(x)= where p and q are ( ) polynomial functions and q(x) 0. The domain of a rat p x q x ional function is the set of all real numbers except the x-values that make the denominator zero.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Example Find the domain of the rational function. 2 16 ( ) 4 x f x x - = -
Image of page 4
Example Find the domain of the rational function. 2 ( ) 36 x f x x = -
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Vertical Asymptotes of Rational Functions
Image of page 6
-4 -3 -2 -1 1 2 3 4 5 -4 -3 -2 -1 1 2 3 4 x y 1 The equation f(x)= x Vertical Asymptote on the y-axis.
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 1 The equation f(x)= Vertical Asymptote on the y-axis. x
Image of page 8
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
Two Graphs with Vertical Asymptotes, one without
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Graphing Calculator 2 f(x)= 9 x x - Input the equation as you see at left. The first graph is Connected Mode. In connected mode, the graphing calculator plots many points and connects the points with "curves." In dot mode, the graphing calculator plots the same points but does not connect them. To change the mode on the calculator press the MODE key then scroll down to the line that says Connected Dot and choose the one that you want to use.
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern