Transformations
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SAT Subject Test in Math II › 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 two units, the new graph is
Since the starting graph was , the final graph is
, or

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

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

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,

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,