Mr. Valsa's Math Page
  • Home
  • AP Calculus AB
    • Course Intro
    • Unit 01: Limits & Continuity >
      • 1.1 Intro to Calculus
      • 1.2 Defining Limits & Using Limit Notation
      • 1.3 Estimating Limit Values from a Graph
      • 1.4 Estimating Limit Values from a Table
      • 1.5 Determining Limits Using Algebraic Properties
      • 1.6 Determining Limits Using Algebraic Manipulation
      • 1.7 Selecting Procedures for Determining Limits
      • 1.8 Squeeze Theorem
      • 1.9 Multiple Representations of Limits
      • 1.10 Exploring Types of Discontinuities
      • 1.11 Defining Continuity
      • 1.12 Confirming Continuity over an Interval
      • 1.13 Removing Discontinuity
      • 1.14 Infinite Limits & Vertical Asymptotes
      • 1.15 Connecting Limits at Infinity & Horizontal Asymptotes
      • 1.16 Intermediate Values Theorem (IVT)
  • AP Calculus BC
    • Course Intro
    • Unit 01: Limits, Continuity & Derivative Rules
    • Unit 02 - Applications of the Derivative
  • PreCalculus
    • Unit 01: Function Analysis >
      • 1.1 Set & Interval Notation
      • 1.2 Function Review
      • 1.3 Domain & Range
      • 1.4 End Behavior & Extrema
      • 1.5 Inc/Dec/Const
      • 1.6 Symmetry
      • 1.7 Function Transformations
      • 1.8 Function Operations
      • 1.9 Inverses
      • 1.10 Piecewise Functions
      • Unit 01 Review Material
    • Unit 02: Polynomial & Rational Functions >
      • 2.1 Solving Polynomials
      • 2.2 Classifying Polynomials
      • 2.3 Complex Numbers
      • 2.4 End Behavior
      • 2.5 Writing Equations of Polynomials
      • 2.6 Solving Rational Equations
      • 2.7 Rational Inequalities
      • 2.8 Types of Discontinuity
      • 2.9 Graphing Rational Functions
      • Unit 02 Review Material
    • Unit 03: Conic Sections >
      • 3.1 Intro to Conic Sections
      • 3.2 Circles
      • 3.3 Ellipses
      • 3.4 Hyperbolas
      • 3.5 Parabolas
      • 3.6 Systems of Conic Sections
      • Unit 03 Review
    • Unit 04: Exponents & Logarithms >
      • 4.1 Exponents & Logarithms
      • 4.2 Evaluating Logarithms
      • 4.3 Solving Exponential & Log Equations
      • 4.4 Growth & Decay Models
      • 4.5 Properties of Logarithms
      • 4.6 Graphing Exponentials
      • Unit 04 Review Material
    • Unit 05: Sequences & Series >
      • 5.1 Arithmetic & Geometric Sequences
      • 5.2 Arithmetic Series
      • 5.3 Finite Geometric Series
      • 5.4 Infinite Geometric Series
      • 5.6 Sigma Notation
      • Unit 05 Review Material
    • Unit 06: Right Triangle Trigonometry >
      • 6.1 Right Angle Trigonometry
      • 6.2 Applications of Trigonometry
      • 6.3 Standard Position, Degrees, Radians
      • 6.4 Coterminal & Reference Angles
      • 6.5 Evaluating Trig Functions
      • 6.6 The Unit Circle
      • 6.7 Inverse Trig
      • 6.8 Law of Sines/Cosines
      • 6.9 Applications Part 2
      • Unit 06 Review Material
    • Unit 07: Graphing Trigonometric Functions >
      • 7.1 Graphing Basic Trig
      • 7.2 Graphing Trig Functions
      • 7.3 Trig Graphs w/ Phase Shifts
      • 7.4 Writing Equations of Sine/Cosine Graphs
      • 7.5 Modeling with Trig
      • 7.6 Graphing Tangent
      • 7.7 Writing Tangent Equations
      • Unit 07 Review Material
    • Unit 08: Trigonometric Identities >
      • 8.1 Complex Fractions
      • 8.2 Simplifying Trig Expressions
      • 8.3 Verifying Identities
      • 8.4 Sum & Difference Identities
      • 8.5 Half & Double Angle Identities
      • 8.6 Trigonometric Equations
      • Unit 08 Review Material
    • Unit 09: Polar Coordinates >
      • 9.1 Intro to Polar
      • 9.2 Polar Equations
      • 9.3 Basic Polar Graphs
      • Unit 09 Review Material
    • Unit 10: Vectors >
      • 10.1 Intro to Vectors
      • 10.2 Vector Addition/Subtraction
      • 10.3 Unit Vectors
      • 10.4 Vector Applications
      • 10.5 Dot Product
      • 10.6 Cross Product
      • Unit 10 Review Material
    • Unit 11: Intro to Calculus >
      • 11.1 Graphical Limits
      • 11.2 Algebraic Limits
      • 11.3 Continuity
    • Semester 2 Review
  • Integrated Math 3
    • Course Intro
    • Unit 01: Analytic Geometry >
      • 1.1 Graphing Lines
      • 1.2 Parallel & Perpendicular
      • 1.3 Distance & Pythagorean Theorem
      • 1.4 Classifying Quadrilaterals
      • Unit 01 Review
    • Unit 02: Geometric Proofs & Modeling >
      • 2.1 Surface Area & Volume
      • 2.2 Density
      • 2.3 Cross Sections
      • Unit 02 Review
    • SAT Practice
  • Contact
  • Unit 02 -

​4.6 Piecewise Functions

4.6_graphing_piecewise_functions_notes.pdf
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4.6_completed_notes.pdf
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4.6_extra_practice.pdf
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4.6_extra_practice_completed.pdf
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4.6_worksheet.pdf
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4.6_worksheet_ans.pdf
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  • Home
  • AP Calculus AB
    • Course Intro
    • Unit 01: Limits & Continuity >
      • 1.1 Intro to Calculus
      • 1.2 Defining Limits & Using Limit Notation
      • 1.3 Estimating Limit Values from a Graph
      • 1.4 Estimating Limit Values from a Table
      • 1.5 Determining Limits Using Algebraic Properties
      • 1.6 Determining Limits Using Algebraic Manipulation
      • 1.7 Selecting Procedures for Determining Limits
      • 1.8 Squeeze Theorem
      • 1.9 Multiple Representations of Limits
      • 1.10 Exploring Types of Discontinuities
      • 1.11 Defining Continuity
      • 1.12 Confirming Continuity over an Interval
      • 1.13 Removing Discontinuity
      • 1.14 Infinite Limits & Vertical Asymptotes
      • 1.15 Connecting Limits at Infinity & Horizontal Asymptotes
      • 1.16 Intermediate Values Theorem (IVT)
  • AP Calculus BC
    • Course Intro
    • Unit 01: Limits, Continuity & Derivative Rules
    • Unit 02 - Applications of the Derivative
  • PreCalculus
    • Unit 01: Function Analysis >
      • 1.1 Set & Interval Notation
      • 1.2 Function Review
      • 1.3 Domain & Range
      • 1.4 End Behavior & Extrema
      • 1.5 Inc/Dec/Const
      • 1.6 Symmetry
      • 1.7 Function Transformations
      • 1.8 Function Operations
      • 1.9 Inverses
      • 1.10 Piecewise Functions
      • Unit 01 Review Material
    • Unit 02: Polynomial & Rational Functions >
      • 2.1 Solving Polynomials
      • 2.2 Classifying Polynomials
      • 2.3 Complex Numbers
      • 2.4 End Behavior
      • 2.5 Writing Equations of Polynomials
      • 2.6 Solving Rational Equations
      • 2.7 Rational Inequalities
      • 2.8 Types of Discontinuity
      • 2.9 Graphing Rational Functions
      • Unit 02 Review Material
    • Unit 03: Conic Sections >
      • 3.1 Intro to Conic Sections
      • 3.2 Circles
      • 3.3 Ellipses
      • 3.4 Hyperbolas
      • 3.5 Parabolas
      • 3.6 Systems of Conic Sections
      • Unit 03 Review
    • Unit 04: Exponents & Logarithms >
      • 4.1 Exponents & Logarithms
      • 4.2 Evaluating Logarithms
      • 4.3 Solving Exponential & Log Equations
      • 4.4 Growth & Decay Models
      • 4.5 Properties of Logarithms
      • 4.6 Graphing Exponentials
      • Unit 04 Review Material
    • Unit 05: Sequences & Series >
      • 5.1 Arithmetic & Geometric Sequences
      • 5.2 Arithmetic Series
      • 5.3 Finite Geometric Series
      • 5.4 Infinite Geometric Series
      • 5.6 Sigma Notation
      • Unit 05 Review Material
    • Unit 06: Right Triangle Trigonometry >
      • 6.1 Right Angle Trigonometry
      • 6.2 Applications of Trigonometry
      • 6.3 Standard Position, Degrees, Radians
      • 6.4 Coterminal & Reference Angles
      • 6.5 Evaluating Trig Functions
      • 6.6 The Unit Circle
      • 6.7 Inverse Trig
      • 6.8 Law of Sines/Cosines
      • 6.9 Applications Part 2
      • Unit 06 Review Material
    • Unit 07: Graphing Trigonometric Functions >
      • 7.1 Graphing Basic Trig
      • 7.2 Graphing Trig Functions
      • 7.3 Trig Graphs w/ Phase Shifts
      • 7.4 Writing Equations of Sine/Cosine Graphs
      • 7.5 Modeling with Trig
      • 7.6 Graphing Tangent
      • 7.7 Writing Tangent Equations
      • Unit 07 Review Material
    • Unit 08: Trigonometric Identities >
      • 8.1 Complex Fractions
      • 8.2 Simplifying Trig Expressions
      • 8.3 Verifying Identities
      • 8.4 Sum & Difference Identities
      • 8.5 Half & Double Angle Identities
      • 8.6 Trigonometric Equations
      • Unit 08 Review Material
    • Unit 09: Polar Coordinates >
      • 9.1 Intro to Polar
      • 9.2 Polar Equations
      • 9.3 Basic Polar Graphs
      • Unit 09 Review Material
    • Unit 10: Vectors >
      • 10.1 Intro to Vectors
      • 10.2 Vector Addition/Subtraction
      • 10.3 Unit Vectors
      • 10.4 Vector Applications
      • 10.5 Dot Product
      • 10.6 Cross Product
      • Unit 10 Review Material
    • Unit 11: Intro to Calculus >
      • 11.1 Graphical Limits
      • 11.2 Algebraic Limits
      • 11.3 Continuity
    • Semester 2 Review
  • Integrated Math 3
    • Course Intro
    • Unit 01: Analytic Geometry >
      • 1.1 Graphing Lines
      • 1.2 Parallel & Perpendicular
      • 1.3 Distance & Pythagorean Theorem
      • 1.4 Classifying Quadrilaterals
      • Unit 01 Review
    • Unit 02: Geometric Proofs & Modeling >
      • 2.1 Surface Area & Volume
      • 2.2 Density
      • 2.3 Cross Sections
      • Unit 02 Review
    • SAT Practice
  • Contact
  • Unit 02 -