Sunday, 25 December 2011

Transformations of Graphs

  •  Edexcel - C1, Algebra and Functions
  • AQA - C1,Algebra and Functions
  • OCR - C1, Coordinate Geometry and Graphs

In this final post of the first chapter, we will discuss how to transform graphs. Four Transformations can be applied to graphs, and we need to be able to draw the resulting graphs from these transformations.

Transformation 1 - y = af(x)
What you do - Multiply each y coordinate of the graph by a.
How this looks graphically - It either squahes the graph vertically, or stretches it out, depending on a.
** This transformation only affects the y coordinates, the x coordinates stay the same.**

Transformation 2 - y=f(x) + a
What you do - Add a to each of the y coordinate.
How this looks graphically - It shifts the graph upwards by a units.
** Again, this transformation only affects the y-coordinates, and if it is y=f(x) - a, then simply the graph shifts downwards**

Transformation 3 - y=f(ax)
What you do - Divide each x-coordinate by a.
How this looks graphically - It Scales the graph by a factor of 1/a, parellel to the x-axis.
** This transformation only affects the x-coordinates**

Transformation 4 - y=f(x + a)
What you do - Subtract a from each x-coordinate.
How this looks graphically - It shifts the graph to the left by a units.
**This transformation only affects the x-coordinates, if it is y =f(x - a), then the graph will shift to the right by a units.**

I have attached one example with my image notes ! Will post another one tomorrow.

Notes on Transformations of Functions
Example 1

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