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Chapter 2: Q 47. (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 4and the absolute minimum is 1.

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 denote a function defined on some intervalI. If there is a numberu in I for which f(x)≤f(u) for all x in I, then f(u)is the absolute maximum of f and I.

If there is a number v inI for which f(x)≥f(v) for all xin I , then f(v)is the absolute minimum offon I.

03

Step 3. Find the absolute maximum. 

The given graph has the closed interval [0,4]as its domain.

We can see from the graph that the given function has maximum value in the interval [0,5]is:

f(3)=4

The largest value of fis f(3)=4.

Therefore, the absolute maximum of the function is 4.

04

Step 4. Find the absolute minimum.

We can see from the graph that the given function has two minimum values in the interval [0,4].

f(1)=1f(4)=3

The smallest value of fis f(1)=1.

Therefore, the absolute minimum of the function is 1.

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Most popular questions from this chapter

The inequality-1<x<3can be written in interval notation as___________.

True or False The independent variable is sometimes

referred to as the argument of the function.

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

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

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)=2x3
See all solutions

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