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Discrete Graph: Isolated Points

publish date: 2026/05/23 18:30:37.478963 UTC

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Consider \(f(x) = 2x + 1\) with domain \(A = \{0,1,2,3\}\). The diagram below shows the four points that make up its graph.

x y

What kind of graph does this function produce?

Correct Answer

Four isolated points: (0,1), (1,3), (2,5), (3,7)

Explanation

When the domain is the finite set \(\{0,1,2,3\}\), the function produces exactly four values and its graph consists of four isolated points: \((0,1), (1,3), (2,5), (3,7)\). Only when the domain is extended to all of \(\mathbb{R}\) does the graph become the continuous straight line \(y = 2x+1\).

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

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