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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 2.3, Problem 3E

a.

To determine

**To fill in the gaps**: with reference to the provided graph

Expert Solution

If f is increasing on an interval, then the y -values of the points on the graph __increase __as the x -values increase. From the graph of f , we see that f is increasing on the interval __[1, 2] __and __[4, 5] __.

**Given information**: if f is increasing on an interval, then the y -values of the points on the graph____ as the x -values increase. From the graph of f , we see that f is increasing on the interval _____ and _____ .

From the provided information, consider,

As f increases the height if the function f ( x ) also increases, thus, y-values of the points on the graph increase as the x-values increase. In the graph provided, f is increasing on the intervals [1, 2] and [4, 5].

Hence, if f is increasing on an interval, then the y -values of the points on the graph __increase __as the x -values increase. From the graph of f , we see that f is increasing on the interval __[1, 2] __and __[4, 5] __.

b.

To determine

**To fill in the gaps**: with reference to the provided graph

Expert Solution

If f is decreasing on an interval, then the y -values of the points on the graph __decrease __as the x -values increase. From the graph of f , we see that f is increasing on the interval __[2, 4] __and __[5, 6] __.

**Given information**: If f is decreasing on an interval, then the y- values of the points on the graph ______ as the x -values increases. From the graph, we see that f is decreasing on the interval ____ and ____.

From the provided information, consider,

As f decreases, the height of the function f ( x ) also decreases, thus, y-values of the points on the graph decrease as the x-values increase. In the graph provided, f is increasing on the intervals [2, 3] and [5, 6].

Hence, if f is decreasing on an interval, then the y -values of the points on the graph __decrease __as the x -values increase. From the graph of f , we see that f is increasing on the interval __[2, 4] __and __[5, 6] __.