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

Verified step by step guidance

1. Recognize that the equation \(x = -4\) represents a vertical line where the x-coordinate is always \(-4\) regardless of the y-coordinate.
2. 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.
3. Draw a straight vertical line passing through all these points at \(x = -4\).
4. Determine the domain: since \(x\) is fixed at \(-4\), the domain is the single value \(\{ -4 \}\).
5. Determine the range: because \(y\) can be any real number, the range is all real numbers, expressed as \((-\infty, \infty)\).

Key Concepts

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.

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.

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.