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Chapter 2: Q 50. (page 90)

In Problems 45鈥�52, for each graph of a function y=f(x), find the absolute maximum and the absolute minimum, if they exist.

Short Answer

Expert verified

The absolute maximum is 4 and the function has no absolute minimum.

Step by step solution

01

Step 1. Given information.

The given graph of the function y=f(x)is:

02

Step 2. Use the concept of absolute maximum and absolute minimum.

Let f denote a function defined on some interval I. If there is a number u in I for which f(x)鈮�f(u) for all x in I, then is the absolute maximum of f and I.

If there is a number v in I for whichf(x)鈮�f(v) for all x in I , then f(v)is the absolute minimum of f on I.

03

Step 3. Find the absolute maximum.

We can see from the graph that the given function has the domain {x-1鈮�x<3}.

We can see from the graph that the given function has maximum value fon its domain is:

f(2)=4

Therefore, the absolute maximum of the function is 4.

04

Step 4. Find the absolute minimum.

The function is approaching infinity at point x=3.

Thus, the largest value of fis not defined.

The function has no absolute minimum value.

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Most popular questions from this chapter

In Problems 7鈥�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

True or False If no domain is specified for a function f, then the domain of fis taken to be the set of real numbers.

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.

g(x)=x3+1

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?

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.

g(x)=4x
See all solutions

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