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A-Level Maths | Graphs & Transformations

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Cubic graphs

  • ax3+bx2+cx+d
  • N-shaped

Quartic graphs

  • ax4+bx3+cx2+dx+e
  • W-shaped

Reciprocal graphs

    • k/x
    • -k/x
    • k/x2
    • -k/x2

Transformations

  • Types of transformations
    • Enlargement (stretch)
    • Translation (movement)
    • Reflection
  • Tips
    • Transformations outside the bracket affect the y-coordinates
    • Transformations inside the bracket affect the x-coordinates
    • When it is inside the bracket, think the OPPOSITE
  • f(x) - original graph
  • f(x) + 21 - original graph has been translated up by 21
  • f(x+21) - original graph has been translated left by 21
  • 2f(x) - y-values have been stretched by scale factor 2
  • f(2x) - x-values have been stretched by scale factor 1/2
  • -f(x) - reflection of the y-values
  • f(-x) - reflection of the x-values

Question 1

Question 2