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Precalc Reference Book

Created in 2015 as a final project in high school

It's a LaTeX book containing most of what we learned in precalc

  • Final.pdf - Final LaTeX output
  • Reference Book.tex - Slightly outdated source code for the PDF

Contents

  • Basic Functions (pg. 5)
    • Linear Function
    • Quadratic Function
    • Cubic Function
    • Reciprocal Function
    • Square Root Function
    • Exponential Function
    • Logarithmic Function
    • Sine Function
    • Cosine Function
    • Absolute Value Function
  • Graphical Transformations (pg. 14)
    • Flipping the y-values over the x-axis and the y-axis
    • Moving y-values left and right on the x-axis
    • Moving the y-values up and down on the y-axis
    • Vertical modifications to the graph
      • Stretch f(x) → af(x) when a > 1
      • Shrink f(x) → af(x) when 0 < a < 1
    • Horizontal modifications to the graph
      • Stretch f(x) → f(x÷c) when c > 1
      • Shrink f(x) → f(x÷c) when 0 < c < 1
  • Function Composition and Inverse (pg. 17)
    • Function Composition
    • Inverse
  • Quadratic Functions (pg. 18)
    • Standard Form
    • Vertex Form
    • Converting from Standard Form to Vertex Form using Completing the Square
  • Power Functions (pg. 19)
    • Direct Variation
    • Indirect Variation
  • Polynomial Functions (pg. 19)
    • Multiplicity
      • Guesstimating a graph
    • Finding the function from zeros
  • Long Division vs. Synthetic Division (pg. 21)
    • Long Divison Example
    • Synthetic Division Example
  • Solving Inequalities With Sign Charts (pg. 22)
  • Exponential and Logarithmic Functions (pg. 22)
    • Solving Exponential Functions
    • Solving Logarithmic Functions
    • Properties of Logs
      • Condensing
      • Expanding
  • Partial Fraction Decomposition (pg. 23)
    • Decompose
    • Sequences and Series
      • Sequences
    • Convergent vs. Divergent Sequences
    • Sum of Finite Series
    • Partial Sum of Infinite Series
  • Trigonometric Functions (pg. 24)
    • Radians
    • Unit Circle
    • Graphs of Cosecant, Secant, and Cotangent
      • Cosecant
      • Secant
      • Cotangent
    • Inverse Sine, Cosine, Tangent
      • Inverse Sine
      • Inverse Cosine
      • Inverse Tangent
    • Evaluating Trigonometry Expressions Using The Unit Circle
    • Sinusoidal Functions
  • Analytic Trigonometry (pg. 31)
    • Reciprocal Identities and Quotient Identities
    • Pythagorean Identities
    • Double Angle Identities
    • Half Angle Identities
    • Power-Reducing Identities
    • Simplifying Trig Functions
    • Solving Trig Equations
    • Proving Trig Identities
    • Law of Sines
    • Law of Cosines
    • Area of a Triangle (SAS and SSS)
  • Application of Trigonometry (pg. 37)
    • Vectors
    • Parametric Equation
    • Polar Coordinates
    • Graphs and Equations of Polar Relations
  • Conic Sections (pg. 43)
    • Parabolas
    • Ellipse
    • Hyperbola

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A LaTeX book created as a final project. Created in 2015

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