Algebra 2 Transformation Rules

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Questions and Answers

What is the result of reflecting a function across the x-axis?

  • f(-x)
  • -f(x) (correct)
  • f(x-a)
  • f(x) + a

What is the result of reflecting a function across the y-axis?

  • f(x+a)
  • f(x) - a
  • -f(x)
  • f(-x) (correct)

What does the expression f(x+a) represent?

  • Vertical shift up
  • Reflection across the x-axis
  • Horizontal shift right
  • Horizontal shift left (correct)

What does the expression f(x-a) represent?

<p>Horizontal shift right (C)</p> Signup and view all the answers

What does f(x) + a represent?

<p>Vertical shift up (C)</p> Signup and view all the answers

What does f(x) - a represent?

<p>Vertical shift down (C)</p> Signup and view all the answers

A vertical stretch is indicated by the condition a > 1.

<p>True (A)</p> Signup and view all the answers

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Study Notes

Reflection Rules

  • Reflection across the x-axis is represented by the equation -f(x), which flips the graph over the x-axis.
  • Reflection across the y-axis is denoted by f(-x), which flips the graph over the y-axis.

Shift Rules

  • A horizontal shift to the left is expressed as f(x+a), moving the graph left by 'a' units.
  • A horizontal shift to the right is shown as f(x-a), moving the graph right by 'a' units.
  • A vertical shift upwards is characterized by f(x) + a, lifting the graph up by 'a' units.
  • A vertical shift downwards is represented by f(x) - a, lowering the graph down by 'a' units.

Stretch Rules

  • A vertical stretch occurs when the function is multiplied by a factor 'a' where a > 1, making the graph steeper.

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