### All College Algebra Resources

## 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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

None of the other choices gives the correct response.

**Correct answer:**

The reflection of the graph of a function about the -axis yields the graph of the function . Therefore, set and substitute for to yield the function

.