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Factoring Practice

x 2 – 16 x 3 + 27 25x 2 + 15. x 2 – 10x + 24 16x 2 -36 27x 3 - 8. Factoring Practice. (x – 4)(x + 4). (x – 6)(x – 4). (x + 3)(x 2 - 3x + 9). 4(2x – 3)(2x + 3). 5(5x 2 + 3). (3x – 2)(9x 2 +6x + 4). 9.2 Graphing Simple Rational Functions. p. 540

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Factoring Practice

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  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

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