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Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
3. Graphs of Functions
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Exercise 1 Page 37

Recall the definitions of an increasing function, a decreasing function, and a constant function.

decreasing

We want to complete the following sentence.

A function f is on an interval when, for any x_1 and x_2 in the interval, x_1 < x_2 implies f(x_1) >f(x_2).

To do this, let's remember the definitions of an increasing function, a decreasing function, and a constant function.

Definition
A function f is increasing on an interval when, for any x_1 and x_2 in the interval, x_1 < x_2 implies that f(x_1) < f(x_2).
A function f is decreasing on an interval when, for any x_1 and x_2 in the interval, x_1 < x_2 implies that f(x_1) > f(x_2).
A function f is constant on an interval when, for any x_1 and x_2 in the interval, f(x_1) = f(x_2).

We can see that the given sentence matches the definition of a decreasing function. With this in mind, let's complete the sentence.

A function f is decreasing on an interval when, for any x_1 and x_2 in the interval, x_1 < x_2 implies f(x_1) >f(x_2).

Subchapter links expand_more
arrow_right Vocabulary and Concept Check p.37
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arrow_right Procedures and Problem Solving p.37-39
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arrow_right Conclusions p.40
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arrow_right Cumulative Mixed Review p.40
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