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Chapter 1: Problem 50

Give an example of a set consisting of two points in the coordinate plane that is not the graph of any function.

Short Answer

Expert verified
The set S = {(2, 3), (2, 5)} is an example of a set consisting of two points in the coordinate plane that is not the graph of any function, as the x-value 2 has two different corresponding y-values, 3 and 5.

Step by step solution

01

Choosing Two Points with the Same x-value

To find a set that is not the graph of a function, we need to choose two points with the same x-value but different y-values. Let us consider the points (2, 3) and (2, 5).
02

Verify that the Set Is Not the Graph of a Function

We have the set of points, S = {(2, 3), (2, 5)}. For the set S to be the graph of a function of x, there should be only one y-value for each x-value. But in this case, the x-value 2 has two different corresponding y-values, 3 and 5. Therefore, S does not satisfy the definition of a function's graph.
03

Conclusion

The set S = {(2, 3), (2, 5)} is an example of a set consisting of two points in the coordinate plane that is not the graph of any function.

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Most popular questions from this chapter

Suppose \(f\) and \(g\) are functions, each with domain of four numbers, with \(f\) and \(g\) defined by the tables below: $$\begin{array}{c|c}x & f(x) \\\\\hline 1 & 4 \\\2 & 5 \\\3 & 2 \\\4 & 3\end{array}$$ $$\begin{array}{c|c}x & g(x) \\\\\hline 2 & 3 \\\3 & 2 \\\4 & 4 \\\5 & 1\end{array}$$ Give the table of values for \(f^{-1} \circ f\).

Suppose \(f\) is a function and a function \(g\) is defined by the given expression. (a) Write \(g\) as the composition of \(f\) and one or two linear functions. (b) Describe how the graph of \(g\) is obtained from the graph of \(f\). \( g(x)=3 f(x)-2\)

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