# College Algebra : Transformations

## Example Questions

### Example Question #11 : Transformations

The graph of a function  is reflected about the -axis, then translated upward  units. Which of the following is represented by the resulting graph?

Explanation:

Reflecting the graph of a function  about the -axis results in the graph of the function

.

Translating this graph upward  results in the graph of the function

.

### Example Question #12 : Transformations

Translate the graph of  upward three units to yield the graph of a function . Which of the following is a valid way of stating the definition of ?

Explanation:

A vertical translation of the graph of a function  by  units yields the graph of the function . A translation in an upward direction is a positive translation, so setting  and , the resulting graph becomes

or

Apply properties of logarithms to rewrite this as

.

### Example Question #13 : Transformations

Reflect the graph of  about the -axis to yield the graph of a function . Which of the following is a valid way of stating the definition of ?