Question

graph the given line. give the domain and range.
2x + 4 = 0

use the graphing tool to graph the line
click to enlarge graph

Explanation:

Step1: Solve for x

To find the equation of the line, we solve \(2x + 4 = 0\) for \(x\). Subtract 4 from both sides: \(2x = -4\). Then divide by 2: \(x = -2\).

Step2: Determine the graph

The equation \(x = -2\) represents a vertical line passing through \(x = -2\) on the x - axis. For a vertical line, the x - value is always - 2, and the y - value can be any real number.

Step3: Find the domain

The domain of a function is the set of all possible x - values. For the line \(x=-2\), the only x - value is - 2. So the domain is \(\{x|x = - 2\}\) (or in interval notation, \([-2,-2]\)).

Step4: Find the range

The range of a function is the set of all possible y - values. Since the line \(x = - 2\) extends infinitely up and down, the y - values can be any real number. So the range is \(\{y|y\in\mathbb{R}\}\) (or in interval notation, \((-\infty,\infty)\)).

Answer:

• Graph: A vertical line passing through \(x=-2\) (all points with \(x = - 2\) and any real \(y\)).
• Domain: \(\{x|x=-2\}\) (or \([-2,-2]\))
• Range: \(\{y|y\in\mathbb{R}\}\) (or \((-\infty,\infty)\))