SSAT Upper Level Quantitative › How to find transformation for an analytic geometry equation
What equation is graphed in the above figure?
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
.
What equation is graphed in the above figure?
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
.
Give the equation graphed in the above figure.
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
Give the equation graphed in the above figure.
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
.
Give the equation graphed in the above figure.
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
.
Give the equation graphed in the above figure.
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
.
If the graph of the equation is reflected about the
-axis, what will the equation of the resulting graph be?
The reflection of the graph of the equation about the
-axis is the graph of the equation
, so replace
with
:
becomes
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.
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
.
If the graph of the equation is reflected about the origin, what will the equation of the resulting graph be?
The reflection of the graph of the equation about the origin is the graph of the equation
, so replace
with
and
with
:
becomes
If the graph of the equation is reflected about the
-axis, what will the equation of the resulting graph be?
The reflection of the graph of the equation about the
-axis is the graph of the equation
, so replace
with
:
becomes