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Chapter 1: Problem 26

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=|x-1|$$

Short Answer

Expert verified
The graph of \(f(x)=|x-1|\) is a V-shaped graph with its vertex at (1,0). A suitable viewing window would be \(x=[-2,4]\) and \(y=[-1,3]\).

Step by step solution

01

Understand the basic absolute value function graph

The absolute value function, \(f(x)=|x|\), has a graph that is a V shape, which opens upward and has its vertex located at the origin (0,0).
02

Graph the shift

The function \(f(x)=|x-1|\) along with the graph \(f(x)=|x|\) shows a simple horizontal shift to the right by 1 unit. The vertex of the graph will be at the point (1,0). This is because every value \(x\) is subtracted by 1 before calculating the absolute value, hence the shift.
03

Choose an appropriate viewing window

An appropriate viewing window should include the vertex (1,0) and part of both arms of the V. Therefore, a window of \(x=[-2,4]\) and \(y=[-1,3]\) would be appropriate.

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Most popular questions from this chapter

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(z\) varies directly as the square of \(x\) and inversely as \(y\) \((z=6 \text { when } x=6 \text { and } y=4 .)\)

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=4+(1 / x)$$

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(y\) is inversely proportional to \(x .(y=7 \text { when } x=4 .)\)

Sketch the graph of the function. $$g(x)=[[x-3]]$$

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=x^{3}-1$$
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