Elementary & Intermediate Algebra
Elementary & Intermediate Algebra
4th Edition
ISBN: 9780134556079
Author: Sullivan, Michael, III, Struve, Katherine R., Mazzarella, Janet.
Publisher: Pearson,
Question
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Chapter E, Problem 1E
To determine

To fill: The blank in the statement “If k is a positive real number, to obtain the graph of y=f(x)+k from the graph of y=f(x), shift the graph of y=f(x) ______ k units. To obtain the graph of y=f(x)k from the graph of y=f(x), shift the graph of y=f(x) ______ k units.”

Expert Solution & Answer
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Answer to Problem 1E

The completed statement is “If k is a positive real number, to obtain the graph of y=f(x)+k from the graph of y=f(x), shift the graph of y=f(x) up k units. To obtain the graph of y=f(x)k from the graph of y=f(x), shift the graph of y=f(x) down k units”.

Explanation of Solution

Result used:

If a positive real number k is added to the output of a function, y=f(x), the graph of the new function, y=f(x)+k, is the graph of f shifted vertically up k units.

If a positive real number k is subtracted from the output of a function, y=f(x), the graph of the new function, y=f(x)k, is the graph of f shifted vertically down k units.

Description:

Consider the function y=f(x)+k, where k is a positive real number.

Clearly, the number k is added to the output of the function y=f(x).

By the above result, the graph of y=f(x)+k is the graph of f shifted vertically up k units.

Similarly, consider the function y=f(x)k, where k is a positive real number.

Clearly, the number k is subtracted from the output of the function y=f(x).

By the above result, the graph of y=f(x)k is the graph of f shifted vertically down k units.

Therefore, the completed statement is “If k is a positive real number, to obtain the graph of y=f(x)+k from the graph of y=f(x), shift the graph of y=f(x) up k units. To obtain the graph of y=f(x)k from the graph of y=f(x), shift the graph of y=f(x) down k units”.

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