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Chapter 2: Q. 9 (page 89)

Concepts and Vocabulary

True or False: A function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2 , we havef(x1)>f(x2)

Short Answer

Expert verified

True

Step by step solution

01

Given information 

A function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2 , we have f(x1)>f(x2)

02

Decreasing and increasing functions

when x values are increasing and f(x) are increasing then it is an increasing function .

When x values are increasing and f(x) values are decreasing then it is a decreasing function

A function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1 < x2 , we have f(x1)>f(x2)is true .

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Most popular questions from this chapter

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

A rectangle has one corner in quadrant I on the graph of y=16-x2, another at the origin, a third on the positive y-axis and the fourth on the positive x-axis. See the figure.

Part (a): Express the area Aof the rectangle as a function of x.

Part (b): What is the domain of A?

Part (c): Graph A=Ax. For what value of xis Alargest?

Concepts and Vocabulary

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, withx1<x2wehavef(x1)<f(x2)

Find the following for each function:

fx=3xx2-1

Part (a):f2

Part (b):f-2

Part (c):f-x

Part (d):-fx

Part (e):fx-2

Part (f):f2x

True or False The cube function is odd and is increasing on the interval (-∞,∞).
See all solutions

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