The domain of a vertical line is a single real number representing the x-coordinate where the line intersects the x-axis, and the range is all real numbers.
Understanding Domain and Range
- Domain: The set of all possible x-values for which the function is defined. In simpler terms, it's all the x-values that the line covers.
- Range: The set of all possible y-values that the function can output. For a line, it is all the y-values the line covers.
Vertical Lines Explained
A vertical line is represented by the equation x = c, where 'c' is a constant. This means that regardless of the y-value, the x-value is always 'c'.
Domain of a Vertical Line
Because the x-value is always 'c', the domain consists of only that single x-value. Therefore, the domain is {c}. For example, if the equation of the vertical line is x = 5, the domain is {5}.
Range of a Vertical Line
A vertical line extends infinitely upwards and downwards. It includes every possible y-value. Therefore, the range is all real numbers, which can be written as (-∞, ∞).
Summary
| Feature | Description | Example (x = 3) |
|---|---|---|
| Equation | x = c (where 'c' is a constant) | x = 3 |
| Domain | {c} (a single x-value) | {3} |
| Range | All real numbers (-∞, ∞) | (-∞, ∞) |
