# SAT II Math II : Transformations

## Example Questions

### Example Question #1 : Coordinate Geometry

Refer to the above figure.

Which of the following functions is graphed?

The correct answer is not given among the other responses.

Explanation:

Below is the graph of :

The given graph is the graph of  shifted 6 units left (that is,  unit right) and 3 units up.

The function graphed is therefore

where . That is,

### Example Question #2 : Coordinate Geometry

Refer to the above figure.

Which of the following functions is graphed?

Explanation:

Below is the graph of :

If the graph of  is translated by shifting each point  to the point , the graph of

is formed. If the graph is then shifted upward by three units, the new graph is

Since the starting graph was , the final graph is

, or,

### Example Question #1 : Transformations

Refer to the above figure.

Which of the following functions is graphed?

Explanation:

Below is the graph of :

If the graph of  is translated by shifting each point  to the point , the graph of

is formed. If the graph is then shifted right by four units, the new graph is

Since the starting graph was , the final graph is

, or

### Example Question #11 : Coordinate Geometry

Refer to the above figure.

Which of the following functions is graphed?

Explanation:

Below is the graph of :

If the graph of  is translated by shifting each point  to the point , the graph of

is formed. If the graph is then shifted down by four units, the new graph is

.

Since the starting graph was , the final graph is

, or

### Example Question #12 : Coordinate Geometry

Refer to the above figure.

Which of the following functions is graphed?

Explanation:

Below is the graph of :

If the graph of  is translated by shifting each point  to the point , the graph of

is formed. If the graph is then shifted right by two units, the new graph is

Since the starting graph was , the final graph is

, or