# 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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