Transformations: Left Or Right - Farwell

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Transformations

Transformations

Transformation

Left or Right

To understand the effects of h, compare the functions y = x2 and y = (x + 3)2. The table below shows the patterns of values.

By looking at both the table of values and the graph, it appears as though h produces a horizontal shift; in this case, h = -3 shifts the parabola 3 units to the left. Expressing the equation in vertex form, y = (x + 3)2 = (x - (-3))2. In general, the graph is shifted h units to the right if h is positive, and h units to the left if h is negative.

In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

*Note: Remember a sign on the inside of the function does the opposite as a sign on the outside of the function. This is because in order to turn f(x + b) into f(x), x = -3 which graphs to the left.Listen ◀︎ Vertex Form Jump to... Jump to... Creation of Michigan Algebra I Pre-Assessment: Linear Multiple Choice Paper Pre-Assessment: Linear Unit Multiple Choice Paper Pre-Assessment: Linear Unit Multiple Choice Key Overview Independent & Dependent Variables Function Notation Solving for a Variable Finding Zeros Slope-Intercept Form Standard Form Point-Slope Form Domain & Range Inverses Parallel & Perpendicular Lines Tables Graphs Applications Solving Graphing Modeling Graphing Solving Using Substitution Solving Using Elimination Modeling Post-Assessment: Linear Multiple Choice Paper Post-Assessment: Linear Unit Multiple Choice Paper Post-Assessment: Linear Unit Multiple Choice Key Paper Post-Assessment: Linear Unit Short Answer Paper Post-Assessment: Linear Unit Short Answer Key Pre-Assessment: Quadratic Multiple Choice Paper Pre-Assessment: Quadratic Unit Multiple Choice Paper Pre-Assessment: Quadratic Unit Multiple Choice Key Overview Characteristics Function Notation Adding & Subtracting Multiplying & Dividing Graphing Using Square Roots Factoring Completing the Square Quadratic Formula Foundations Vertex Form Factored Form Standard Form Domain & Range Inverses Tables Graphs Applications Which Function Is It? Post-Assessment: Quadratic Multiple Choice Paper Post-Assessment: Quadratic Unit Multiple Choice Paper Post-Assessment: Quadratic Unit Multiple Choice Key Paper Post-Assessment: Quadratic Unit Short Answer Paper Post-Assessment: Quadratic Unit Short Answer Key Pre-Assessment: Polynomial Multiple Choice Paper Pre-Assessment: Polynomial Unit Multiple Choice Paper Pre-Assessment: Polynomial Unit Multiple Choice Key Overview Characteristics Foundations Graphical Behavior Domain & Range Transformations Inverses Graphically Factor by Grouping Factoring Special Patterns Tables Graphs Applications Which Function Is It? Post-Assessment: Polynomial Multiple Choice Paper Post-Assessment: Polynomial Unit Multiple Choice Paper Post-Assessment: Polynomial Unit Multiple Choice Key Paper Post-Assessment: Polynomial Unit Short Answer Paper Post-Assessment: Polynomial Unit Short Answer Key Pre-Assessment: Power & Exponential Multiple Choice Paper Pre-Assessment: Power & Exponential Unit Multiple Choice Paper Pre-Assessment: Power & Exponential Unit Multiple Choice Key Overview Power & Exponential Functions Graphing Inverses Multipying & Dividing Rules Remaining Power Rules Zero & Negative Exponents Fractional Exponents Overview Multiplying & Dividing Adding & Subtracting Solving Equations Graphing Graphical Behavior Transformations Domain & Range Inverses Tables Graphs Exponential Growth Exponential Decay Compound Interest Which Function Is It? Post-Assessment: Power & Exponential Multiple Choice Paper Post-Assessment: Power & Exponential Unit Multiple Choice Paper Post-Assessment: Power & Exponential Unit Multiple Choice Key Paper Post-Assessment: Power & Exponential Unit Short Answer Paper Post-Assessment: Power & Exponential Unit Short Answer Key Pre-Assessment: Bivariate Multiple Choice Paper Pre-Assessment: Bivariate Unit Multiple Choice Paper Pre-Assessment: Bivariate Unit Multiple Choice Key Overview Displaying Data Plotting Data Pearson's Correlation Coefficient Linear Regression Piecewise Absolute Value Recursive Applications Which Function Is It? Post-Assessment: Bivariate Multiple Choice Paper Post-Assessment: Bivariate Unit Multiple Choice Paper Post-Assessment: Bivariate Unit Multiple Choice Key Paper Post-Assessment: Bivariate Unit Short Answer Paper Post-Assessment: Bivariate Unit Short Answer Key Algebra I Final Exam Algebra I Final Exam Key Factored Form ▶︎ Skip Table of contents

Table of contents

• Transformation
  • Up or Down
  • Left or Right
• Effects of "a"
  • Reflecting Over the x-axis
• Summary of the Rules
• Equations
• Interactive Activity
• Interactive Practice
• Guided Practice
• Practice
  • Answer Key
• Sources