Module 1: Function Transformations

 

Lesson 1 Summary

 

The diagram shows a parabola opening down on a coordinate grid. Four arrows point from the parabola. The arrow pointing up is labelled k > 0, the arrow pointing down is labelled k < 0, the arrow pointing left is labelled h < 0, and the arrow pointing right is labelled h > 0.

A transformation is a change in the shape or position of a figure or relation. A translation is a type of transformation that causes a “slide” in the graph. The new graph is the same size, shape, and orientation as the original but in a different position.

 

In a graph of the form y − k = f(x − h), k is the vertical translation from y = f(x). If k > 0, the translation is upwards. If k < 0, the translation is downwards.

 

In a graph of the form y − k = f(x − h), h is the horizontal translation from y = f(x). If h > 0, the translation is to the right. If h < 0, the translation is to the left.

 

 

 

 

 

You may find it useful to keep a summary of the different transformations you learn in this module using a table similar to the following.

 

Parameter Type of Transformation Effect on Graph
     
     
     
     
     
     
     

 

In the next lesson you will begin to look at reflections of a function.