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ET 2.6: Find the domain.

ET 2.6: Find the domain. The domain is helpful in finding vertical asymptotes. x = -2. x = -3. x = 1. Given D(x) = 0 produces Vertical Asymptotes: If factor doesn’t cancel with N(x). Hole: If factor cancels with N(x). D(x) = 0 x 2 + 4x + 3 = 0.

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ET 2.6: Find the domain.

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  1. ET 2.6: Find the domain. The domain is helpful in finding vertical asymptotes. x = -2 x = -3 x = 1

  2. Given • D(x) = 0 produces • Vertical Asymptotes: If factor doesn’t cancel with N(x). • Hole: If factor cancels with N(x). D(x) = 0 x2 + 4x + 3 = 0 (x + 1)(x + 3)=0 Vertical Asymptote (x + 1)=0 (x + 3)=0 Hole x = -1 x = -3

  3. Horizontal Asymptotes: Start by looking at the degree of N(x) & D(x). < = Deg. Deg N(x) D(x) > Deg Deg N(x) D(x) Deg Deg N(x) D(x) y = 0 (x-axis) NONE (Oblique asymptote & need to divide) y = an/bn (Fraction of Leading Coefficients.)

  4. NONE (Oblique asymptote & need to divide) 3x 3x3 + 0x2 - 3x 3x Ignore the REMAINDER y = 3x

  5. Find the equations of all V.A., H.A. & Obliques 1 0 0 y = 5 y = 0 0 0

  6. Graph: VA: x = 3 y = 1 y – int: (Let x=0) HA: Hole @ x = -2 0 OB: x – int: (Let y=0)

  7. Assignment 2.6 Graph: Include intercepts, asymptotes, holes # 27-46 asymptotes only {27, 31, 35, 39, 43 (everything)} #51 – 64 , asymptotes only #87,88 Everything Means: Asymptotes x & y intercepts Domain Holes graph • Three Fudge #77

  8. Oblique Asymptotes y = x + 3

  9. Oblique Asymptote y = x

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