Section
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Content
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Suggested Problems
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Section 6.1
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- Translation of conic sections
- Equations of translation
- Standard forms for conic sections
- Parabola
- Type I: Axis of symmetry parallel to x-axis
- Type II: Axis of symmetry parallel to y-axis
- Ellipse
- Type I: Major axis parallel to x-axis
- Type II: Major axis parallel to y-axis
- Hyperbola
- Type I: Transverse axis parallel to x-axis
- Type II: Transverse axis parallel to y-axis
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Page 198: 7, 8, 9, 10, 11, 12, 21, 22, 23, 25
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Section 6.3
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- Equations of rotation
- x = x' cos θ - y' sin θ
- y = x' sin &theta' + y' cos &theta'
- Transform Quadratic Equation by Rotation
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Page 211: 5, 7, 9
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Section 6.4
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- General second order equation
- Rotate Equation to Eliminate xy term
- Case A = C
- Case A ≠ C
- tan 2θ = B/(A-C)
- Reference triange for angle 2θ
- Trig half angle formulas for cos θ and sin θ
- Discrimant B2 - 4AC
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Page 220: 1, 2, 4, 5, 9
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Section 7.1
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- Definition of Symmetry wrt Line
- Definition of Symmetry wrt Point
- Tests for Symmetry
- Symmetry wrt y-axis
- Symmetry wrt x-axis
- Symmetry wrt origin
- Symmetry wrt line y=x
- Intercepts
- x-axis
- Roots of factors of numerator
- y-axis
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Page 232: 1-4, 11, 13, 17, 19, 21, 23, 27, 28
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Section 7.2
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- Sketching Polynomial Equations
- Fundamental Theorem of Algebra
- Behavior of Graphs near Intercepts
- Factors of Form (x-a)n
- Odd power of n
- Even power of n
- End Behavior
- Sketching Graph
- Symmetry
- Intercepts
- Behavior of Graphs near Intercepts
- End Behavior
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Page 243: 1, 5, 9, 13, 27, 28, 29
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Section 7.3
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- Rational Functions
- Asymptotes
- Vertical
- Roots of factors of denominator
- Horizonatal
- Case Degree Numerator < Degree Denominator
- Case Degree Numerator = Degree Denominator
- Case Degree Numerator > Degree Denominator
- Slant
- Degree Numerator = Degree Denominator + 1
- Divide Numerator by Denominator Longhand
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Page 255: 1, 3, 9, 11, 13, 15, 17
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Section 7.4
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- Sketching the Graphs of Rational Functions
- Symmetry
- Intercepts
- Vertical Asymptotes
- Horizonatal Asymptotes
- Slant Asymptotes
- Interval (x-axis) of Constant Sign
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Page 264: 1, 7, 13, 15, 16, 17, 19, 20
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Section 7.5
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- Equations with Radicals
- Domain Restrictions
- Graph y = square root (p(x))
- Graph auxillary function z = p(x)
- Graph y = square root (z)
- Graph y2 = p(x)
- Graph auxillary function z = p(x)
- Graph y = ± square root (z)
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Page 273: 1, 5, 7, 11, 15
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