2. Unit 2: Transforming and Graphing Functions
  3. Lesson 4: Vertical Stretches, Compressions, and Reflections

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Vertical Stretches, Compressions, and Reflections

Source: Running Stairs - RyanJLane/E+/Getty Images

Graphing Functions Using Transformations

Types of Transformations

 

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Lesson Goals

  • Describe how a reflection in the \(x\)-axis affects a function, and express this type of reflection in function notation.
  • Describe how a vertical stretch or compression affects a function, and express this type of transformation in function notation.
  • Sketch graphs by applying a reflection in the \(x\)-axis, and/or a vertical stretch or compression to a known graph of a function.
  • Identify the domain and range of a function after a vertical stretch or compression and/or reflection in the \(x\)-axis.
  • Compare reflections in the \(x\)-axis with reflections in the \(y\)-axis, and compare vertical stretches/compressions to horizontal stretches/compressions.

Try This

The function \(g(x)\) represents the time it takes a runner to complete a \(5\) km race at an average speed of \(x\) km/h.

Sketch the graph of \(g(x)\).