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Chapter 2: Q 48. (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 minimum is 1 and there is no absolute maximum.

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 fdenote 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 f(u)is the absolute maximum of fand I.

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

03

Step 3. Find the absolute maximum. 

We can see from the graph that the given function has the domain {x0鈮�x<3,x鈮�2}.

Here we are excluding 2 from the domain because of the "hole" at (2,4).

There is no absolute maximum.

The reason being, as we trace the graph getting closer to the point (2,4), there is no single largest value.

04

Step 4. Find the absolute minimum.

We can see from the graph that the given function has a minimum value at its domain is:

f(0)=1

The smallest value of fisf(0)=1.

Therefore, the absolute minimum of the function is 1.

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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

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.

h(x)=x-2

match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

In March 2011, Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge -\(13.55

Distribution charge

First 20therms-0.1473/therm

Next 30therm -\)0.0579/therm

Over 50therm -\(0.0519/therm

Gas supply charge-\)0.51/therm

(a) What is the charge for using 40therms in a month?

(b) What is the charge for using 150therms in a month?

(c) Develop a model that gives the monthly charge Cfor x therms of gas.

(d) Graph the function found in part (c).

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function
See all solutions

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