Pre-Calculus

Pre-Calculus Topics covered by …and Math Tutoring

  • Graphing Equations
  • Intercepts of a Graph
  • Points of Intersection
  • Symmetry of a Graph
  • Mathematical Models
  • Slope
  • Equations of Lines
  • Ratios and Rates of Change
  • Graphing Linear Models
  • Parallel and Perpendicular Lines
  • Functions and Function Notation
  • Domain and Range
  • Graph of a Function
  • Transformations of Functions
  • Fitting a Model to Data
  • Linear, Quadratic, Trigonometric
  • The Tangent Line Problem
  • The Area Problem
  • An Introduction to Limits
  • Limits That Fail to Exist
  • Properties of Limits
  • Strategies for Finding Limits
  • Continuity at a Point and on an Open Interval
  • One-Sided Limits and Continuity on a Closed Interval
  • Properties of Continuity
  • The Intermediate Value Theorem
  • Infinite Limits
  • Vertical Asymptotes
  • DIFFERENTIATION
    • The Tangent Line Problem
    • The Derivative of a Function
    • Sketching a Derivative Based on the Graph of f(x)
    • Differentiability and Continuity
    • The Constant Rule
    • The Power Rule
    • The Constant Multiple Rule
    • The Sum and Difference Rule
    • Derivatives of Sine and Cosine Functions
    • Rates of Change
    • The Product Rule
    • The Quotient Rule
    • Derivatives of Trigonometric Functions
    • Higher-Order Derivatives
    • Position, Velocity, Acceleration Functions
    • The Chain Rule
    • The General power Rule
    • Trigonometric Functions and the Chain Rule
    • Implicit Differentiation
    • Related Rates
    • Extrema of a Function
    • Relative Extrema and Critical Numbers
    • Extrema on a Closed Interval
    • Rolle’s Theorem
    • The Mean Value Theorem
    • Increasing and Decreasing Functions
    • The First Derivative Test
    • Concavity
    • Points of Inflection
    • The Second Derivative Test
    • Limits at Infinity
    • Horizontal Asymptotes
    • Curve-Sketching Techniques
    • Applied Minimum and Maximum Problems (Optimization)
    • Calculating Differentials
    • Linear Approximations
    • Error Propagation
    • Business and Economics Applications

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