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Chapter 2: Q 92. (page 92)

Suppose that a friend of yours does not understand the idea of increasing and decreasing functions. Provide an explanation, complete with graphs, that clarifies the idea.

Short Answer

Expert verified

Increasing function:

A function fis said to be increasing on an interval Iif there exists xand ysuch that x<y, then f(x)≤f(y).

Decreasing function:

A function fis said to be decreasing on an interval Iif there exists xand ysuch that x<y, then f(x)≥f(y).

Step by step solution

01

Step 1. Define increasing function along with graph.

A function f(x)is said to be increasing on an interval Iif there exists two numbers xand yin Isuch that x<y, then f(x)≤f(y).

The required graph is shown below:

02

Step 2. Define decreasing function along with graph.

A function f(x)is said to be decreasing on an interval Iif there exists two numbers xand yin Isuch that x<y, then f(x)≥f(y).

The required graph is shown below:

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Most popular questions from this chapter

A rectangle is inscribed in a circle of radius of 2. See the figure. Let P=x,ybe the point in quadrant I that is a vertex of the rectangle and is on the circle.

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

Part (b): Express the perimeter pof the rectangle as a function of x.

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

Part (d): Graph p=px. For what value ofxis p largest?

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 right triangle has one vertex on the graph of y=9-x2,x>0, at x,y, another at the origin, and the third on the positive x-axis at x,0. Express the area Aof the triangle as a function of x.

The set of all images of the elements in the domain of a function is called the _________.

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x-13+2
See all solutions

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