A-Level Maths | Graphs & Transformations

Cubic graphs

• ax³+bx²+cx+d
• N-shaped

Quartic graphs

• ax⁴+bx³+cx²+dx+e
• W-shaped

Reciprocal graphs

• y = k/x
• y = -k/x
• y = k/x²
• y = -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

Question 3

Question 4