SSAT Upper Level Math : Transformation

Example Questions

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Example Question #1 : Transformation

Give the equation graphed in the above figure.

Explanation:

The graph below is the graph of the absolute value function , which pairs each -coordinate with its absolute value.

The given graph is the same as the above graph, except that each -coordinate is paired with the -coordinate three times that with which it is paired in the above graph. Therefore, the equation graphed is

or

Example Question #2 : Transformation

If the graph of the equation  is shifted right three units on the coordinate plane, what will be the equation of the resulting graph?

Explanation:

The graph of a function  shifted right three units is the graph of . In this graph, , so the graph formed by the transformation is

The correct equation is .

Example Question #3 : Transformation

If the graph of the equation  is reflected about the origin, what will the equation of the resulting graph be?

Explanation:

The reflection of the graph of the equation  about the origin is the graph of the equation , so replace  with  and  with :

becomes

Example Question #4 : Transformation

If the graph of the equation  is reflected about the -axis, what will the equation of the resulting graph be?

Explanation:

The reflection of the graph of the equation  about the -axis is the graph of the equation , so replace  with :

becomes

Example Question #5 : Transformation

If the graph of the equation  is reflected about the -axis, what will the equation of the resulting graph be?

Explanation:

The reflection of the graph of the equation  about the -axis is the graph of the equation , so replace  with :

becomes

Example Question #6 : Transformation

If the graph of the equation  is reflected about the origin, what will the equation of the resulting graph be?

None of the other responses gives a correct answer.

Explanation:

The reflection of the graph of the equation  about the origin is the graph of the equation , so replace  with  and  with :

becomes

The absolute values of two expressions that are each other's opposites are equal, so  is equivalent to . The expression can be rewritten as

.

Example Question #7 : Transformation

Give the equation graphed in the above figure.

Explanation:

The graph below is the graph of the absolute value function , which pairs each -coordinate with its absolute value.

The given graph is the above graph shifted right five units and upward three units. The graph of any function  shifted right five units and upward three units is , so the correct response is .

Example Question #8 : Transformation

If the graph of the equation  is shifted downward seven units on the coordinate plane, what will be the equation of the resulting graph?

Explanation:

The graph of a function  shifted downward seven units is the graph of . In this graph, , so the graph formed by the transformation is that of the equation

Example Question #9 : Transformation

Give the equation graphed in the above figure.

Explanation:

The graph below is the graph of the absolute value function , which pairs each -coordinate with its absolute value.

The given graph is the above graph shifted right two units. The graph of  shifted right two units is , so the correct response is .

Example Question #10 : Transformation

What equation is graphed in the above figure?