College Algebra : Transformations

Study concepts, example questions & explanations for College Algebra

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Example Questions

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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?

Possible Answers:

Correct answer:

Explanation:

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 #62 : Graphs

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 ?

Possible Answers:

Correct answer:

Explanation:

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 #11 : 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 ?

Possible Answers:

None of the other choices gives the correct response.

Correct answer:

Explanation:

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

.

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