Reflections of Graphs (DP IB Analysis & Approaches (AA)) : Revision Note

Reflections of Graphs

What are reflections of graphs?

• When you alter a function in certain ways, the effects on the graph of the function can be described by geometrical transformations

• For a reflection:

  • the graph is flipped about one of the coordinate axes

    • Its orientation changes

  • the size of the graph remains unchanged

• A particular reflection is specified by an axis of symmetry:

  • 

    • This is the x-axis

  • 

    • This is the y-axis

What effects do horizontal reflections have on the graphs and functions?

• A horizontal reflection of the graph about the y-axis is represented by 

  • 

• The x-coordinates change

  • Their sign changes

• The y-coordinates stay the same

• The coordinates become 

• Horizontal asymptotes stay the same

• Vertical asymptotes change

  • becomes 

What effects do vertical reflections have on the graphs and functions?

• A vertical reflection of the graph  about the x-axis is represented by

  • 

  • This is often rearranged to 

• The x-coordinates stay the same

• The y-coordinates change

  • Their sign changes

• The coordinates become 

• Horizontal asymptotes change

  • becomes 

• Vertical asymptotes stay the same