How to find transformation for an analytic geometry equation

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SSAT Upper Level Quantitative › How to find transformation for an analytic geometry equation

Questions 1 - 10
1

Function 2

What equation is graphed in the above figure?

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 .

2

Function 1

What equation is graphed in the above figure?

Explanation

The least integer function, or celing function, , pairs each value of with the least integer greater than or equal to . Its graph is below.

Ceiling function

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

3

Function

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.

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

4

Function

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.

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 .

5

Function

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.

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 .

6

Function

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.

Absolute value graph

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

7

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

8

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

.

9

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

10

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

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