How to find transformation for an analytic geometry equation - SSAT Upper Level Quantitative
Card 0 of 48
What equation is graphed in the above figure?
What equation is graphed in the above figure?
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The greatest integer function, or floor function, 
, pairs each value of 
with the greatest integer less than or equal to 
. Its graph is below.
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 
.
The greatest integer function, or floor function,
The given graph is the above graph shifted downward four units. The graph of any function
If the graph of the equation 
is reflected about the 
-axis, what will the equation of the resulting graph be?
If the graph of the equation
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The reflection of the graph of the equation 
about the 
-axis is the graph of the equation 
, so replace 
with 
:
becomes
The reflection of the graph of the equation
becomes
What equation is graphed in the above figure?
What equation is graphed in the above figure?
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The least integer function, or celing function, 
, pairs each value of 
with the least integer greater than or equal to 
. Its graph is below.
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 
.
The least integer function, or celing function,
The given graph is the above graph shifted upward four units. The graph of any function
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
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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 
.
The graph below is the graph of the absolute value function
The given graph is the above graph shifted right five units and upward three units. The graph of any function
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
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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 
.
The graph below is the graph of the absolute value function
The given graph is the above graph shifted right two units. The graph of
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
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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
The graph below is the graph of the absolute value function
The given graph is the same as the above graph, except that each
or
If the graph of the equation 
is shifted right three units on the coordinate plane, what will be the equation of the resulting graph?
If the graph of the equation
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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 
.
The graph of a function
The correct equation is
If the graph of the equation 
is shifted downward seven units on the coordinate plane, what will be the equation of the resulting graph?
If the graph of the equation
Tap to see back →
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
The graph of a function
If the graph of the equation 
is reflected about the 
-axis, what will the equation of the resulting graph be?
If the graph of the equation
Tap to see back →
The reflection of the graph of the equation 
about the 
-axis is the graph of the equation 
, so replace 
with 
:
becomes
The reflection of the graph of the equation
becomes
If the graph of the equation 
is reflected about the origin, what will the equation of the resulting graph be?
If the graph of the equation
Tap to see back →
The reflection of the graph of the equation 
about the origin is the graph of the equation 
, so replace 
with 
and 
with 
:
becomes
The reflection of the graph of the equation
becomes
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
Tap to see back →
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 upward five units. The graph of any function shifted upward five units is 
, so the correct response is 
.
The graph below is the graph of the absolute value function
The given graph is the above graph shifted upward five units. The graph of any function
If the graph of the equation 
is reflected about the origin, what will the equation of the resulting graph be?
If the graph of the equation
Tap to see back →
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
.
The reflection of the graph of the equation
becomes
The absolute values of two expressions that are each other's opposites are equal, so
What equation is graphed in the above figure?
What equation is graphed in the above figure?
Tap to see back →
The greatest integer function, or floor function, , pairs each value of with the greatest integer less than or equal to . Its graph is below.
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 .
The greatest integer function, or floor function,
The given graph is the above graph shifted downward four units. The graph of any function
If the graph of the equation is reflected about the -axis, what will the equation of the resulting graph be?
If the graph of the equation
Tap to see back →
The reflection of the graph of the equation about the -axis is the graph of the equation , so replace with :
becomes
The reflection of the graph of the equation
becomes
What equation is graphed in the above figure?
What equation is graphed in the above figure?
Tap to see back →
The least integer function, or celing function, , pairs each value of with the least integer greater than or equal to . Its graph is below.
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 .
The least integer function, or celing function,
The given graph is the above graph shifted upward four units. The graph of any function
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
Tap to see back →
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 .
The graph below is the graph of the absolute value function
The given graph is the above graph shifted right five units and upward three units. The graph of any function
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
Tap to see back →
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 .
The graph below is the graph of the absolute value function
The given graph is the above graph shifted right two units. The graph of
Give the equation graphed in the above figure.
Give the equation graphed in the above figure.
Tap to see back →
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
The graph below is the graph of the absolute value function
The given graph is the same as the above graph, except that each
or
If the graph of the equation is shifted right three units on the coordinate plane, what will be the equation of the resulting graph?
If the graph of the equation
Tap to see back →
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 .
The graph of a function
The correct equation is
If the graph of the equation is shifted downward seven units on the coordinate plane, what will be the equation of the resulting graph?
If the graph of the equation
Tap to see back →
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
The graph of a function