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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 26
Chapter 3, Problem 26

Graph each line. Give the domain and range. x = -4

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Recognize that the equation \(x = -4\) represents a vertical line where the x-coordinate is always \(-4\) regardless of the y-coordinate.
To graph the line, plot points where \(x\) is \(-4\) and \(y\) can be any real number, for example, \((-4, 0)\), \((-4, 1)\), \((-4, -1)\), etc.
Draw a straight vertical line passing through all these points at \(x = -4\).
Determine the domain: since \(x\) is fixed at \(-4\), the domain is the single value \(\{ -4 \}\).
Determine the range: because \(y\) can be any real number, the range is all real numbers, expressed as \((-\infty, \infty)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Graphing Vertical Lines

A vertical line is represented by an equation of the form x = a constant. It passes through all points where the x-coordinate is the same, regardless of the y-coordinate. For x = -4, the line is vertical and crosses the x-axis at -4.
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Domain of a Function or Relation

The domain is the set of all possible x-values for which the relation or function is defined. For a vertical line like x = -4, the domain is a single value, x = -4, since the line only includes points where x is -4.
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Range of a Function or Relation

The range is the set of all possible y-values that the relation or function can take. For the vertical line x = -4, the range includes all real numbers because y can be any value along the vertical line.
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