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Example Questions
Example Question #11 : Transformations
The graph of a function is reflected about the -axis, then translated upward units. Which of the following is represented by the resulting graph?
Reflecting the graph of a function about the -axis results in the graph of the function
.
Translating this graph upward results in the graph of the function
.
Example Question #12 : Transformations
Translate the graph of upward three units to yield the graph of a function . Which of the following is a valid way of stating the definition of ?
A vertical translation of the graph of a function by units yields the graph of the function . A translation in an upward direction is a positive translation, so setting and , the resulting graph becomes
or
Apply properties of logarithms to rewrite this as
.
Example Question #13 : Transformations
Reflect the graph of about the -axis to yield the graph of a function . Which of the following is a valid way of stating the definition of ?
None of the other choices gives the correct response.
The reflection of the graph of a function about the -axis yields the graph of the function . Therefore, set and substitute for to yield the function
.