1 / 10

Understanding Rational Functions & Hyperbolas

Learn about rational functions, hyperbolas, asymptotes, branches, graphs, domains, ranges, and more to enhance your math knowledge. Practice factoring and graphing to master these concepts.

karleigh-walls
Télécharger la présentation

Understanding Rational Functions & Hyperbolas

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. x2 – 16 x3 + 27 25x2 + 15 x2 – 10x + 24 16x2 -36 27x3 - 8 Factoring Practice (x – 4)(x + 4) (x – 6)(x – 4) (x + 3)(x2 - 3x + 9) 4(2x – 3)(2x + 3) 5(5x2 + 3) (3x – 2)(9x2 +6x + 4)

  2. 9.2 Graphing Simple Rational Functions p. 540 What is the general form of a rational function? What does the h & k tell you? What does the graph of a hyperbola look like? What does the graph of ax+b/cx+d tell you? What information does the domain & range tell you?

  3. Rational Function • A function of the form where p(x) & q(x) are polynomials and q(x)≠0.

  4. Hyperbola x=0 • A type of rational function. • Has 1 vertical asymptote and 1 horizontal asymptote. • Has 2 parts called branches. (blue parts) They are symmetrical. We’ll discuss 2 different forms. y=0

  5. Hyperbola (continued) • One form: • Has 2 asymptotes: x=h (vert.) and y=k (horiz.) • Graph 2 points on either side of the vertical asymptote. • Draw the branches.

  6. Hyperbola (continued) • Second form: • Vertical asymptote: Set the denominator equal to 0 and solve for x. • Horizontal asymptote: • Graph 2 points on either side of the vertical asymptote. Draw the 2 branches.

  7. Ex: Graph State the domain & range. Vertical Asymptote: x=1 Horizontal Asymptote: y=2 x y -5 1.5 -2 1 2 5 4 3 Left of vert. asymp. Right of vert. asymp. Domain: all real #’s except 1. Range: all real #’s except 2.

  8. Ex: GraphState domain & range. Vertical asymptote: 3x+3=0 (set denominator =0) 3x=-3 x= -1 Horizontal Asymptote: x y -3 .83 -2 1.33 0 -.67 2 0 Domain: All real #’s except -1. Range: All real #’s except 1/3.

  9. What is the general form of a rational function? • What does the h & k tell you? Asymptotes are x = h, y = k • What does the graph of a hyperbola look like? Two symmetrical branches in opposite quadrants. • What does the graph of ax+b/cx+d tell you? cx+d = 0 is the vertical asymptote and y = a/c is the horizontal asymptote • What information does the domain & range tell you? Domain tells what numbers can be used for x and the range is the y numbers when put into the equation.

  10. Assignment p. 543 12-22, 24-28 even, 32-38 even

More Related