Chapter 1.4, Problem 1E

To determine

To name the types of rigid transformations

Explanation of Solution

Horizontal shifts, Vertical shifts and reflections are called rigid transformations. It is because when these operations are performed on the base graph the basic shape of the base graph remains unaltered.

1. Horizontal shift:

Example with Graph:

  

The above graph shows the horizontal shift of 3 units on both left side and right side of the base equation $y=x^2$ .

2. Vertical shift:

Example with Graph:

  

The above graph shows the vertical shift of 3 units on both upwards and downward for the base equation $y=x^2$ .

3. Reflection:

Example with Graph:

  

The above graph shows the reflection about x-axis for the base equation $y=x^2$ .

Conclusion:

From all the graphs it is clear that the shape of the base graph never got distorted.