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Functions and Their Graphs Help (page 2)

based on 8 ratings
By — McGraw-Hill Professional
Updated on Oct 4, 2011

Increasing, Decreasing, and Constant Intervals

Increasing and Decreasing

A function is increasing on an interval if moving toward the right in the interval means the graph is going up. A function is decreasing on an interval if moving toward the right in the interval means the graph is going down. The function whose graph is in Figure 3.6 is increasing from x = −3 to x = 0 as well as to the right of x = 2. It is decreasing to the left of x = −3 and between x = 0 and x = 2. Using interval notation, we say the function is increasing on the intervals (−3, 0) and (2, ∞) and decreasing on the intervals (−∞, −3) and (0, 2). For reasons covered in calculus, parentheses are used for the interval notation.

Functions and Their Graphs Examples

Fig. 3.6 .

Constant

A function is constant on an interval if the y -values do not change. This part of the graph will be part of a horizontal line.

Examples

Determine the intervals on which the functions are increasing, decreasing or constant.

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    Functions and Their Graphs Examples

    Fig. 3.7 .

    This function is increasing on (−5, −2) and (4, 5). It is decreasing on (−2, 2) and constant on (2, 4).

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    Functions and Their Graphs Examples

    Fig. 3.8 .

    The function is increasing on all of its domain, (0, ∞).

Find practice problems and solutions for these concepts at Functions and Their Graphs Practice Problems.

Find practice problems and solutions for these concepts at Functions and Their Graphs Practice Test.

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