SSAT Upper Level Math : How to find transformation for an analytic geometry equation

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : How To Find Transformation For An Analytic Geometry Equation

Function

Give the equation graphed in the above figure.

Possible Answers:

Correct answer:

Explanation:

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

Absolute value graph

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 : How To Find Transformation For An Analytic Geometry Equation

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

Possible Answers:

Correct answer:

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 #245 : Geometry

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

Possible Answers:

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

Example Question #246 : Geometry

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

Possible Answers:

Correct answer:

Explanation:

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

becomes

Example Question #247 : Geometry

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

Possible Answers:

Correct answer:

Explanation:

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

becomes

Example Question #248 : Geometry

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

Possible Answers:

None of the other responses gives a correct answer.

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 #3 : How To Find Transformation For An Analytic Geometry Equation

Function

Give the equation graphed in the above figure.

Possible Answers:

Correct answer:

Explanation:

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

Absolute value graph

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 #4 : How To Find Transformation For An Analytic Geometry Equation

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

Possible Answers:

Correct answer:

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 #5 : How To Find Transformation For An Analytic Geometry Equation

Function

Give the equation graphed in the above figure.

Possible Answers:

Correct answer:

Explanation:

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

Absolute value graph

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 #6 : How To Find Transformation For An Analytic Geometry Equation

Function 2

What equation is graphed in the above figure?

Possible Answers:

Correct answer:

Explanation:

The greatest integer function, or floor function, , pairs each value of  with the greatest integer less than or equal to . Its graph is below.

Floor function

The given graph is the above graph shifted downward four units. The graph of any function  shifted downward four units is , so the given graph corresponds to equation .

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