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Chapter 2: Q 50. (page 90)

In Problems 45–52, 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)≤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)≤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≤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 7–18, 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

Exploration Graph y=x3. Then on the same screen graph y=(x-1)3+2. Could you have predicted the result?

Determine whether each relation represents a function. For each function, state the domain and range.

4,-1,2,1,4,2

Exploration Graph y=x. Then on the same screen graph y=-x. What pattern do you observe? Now try y=2x+1 and y=2(-x)+1. What do you conclude?

In Problems 19-26,write the function whose graph is the graph of y=x3but is:

Shifted to the right4 units
See all solutions

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