The function h(x) = 0.5x + 9 is a linear function, which means it can be represented with a straight line on a graph.
Domain
The domain of a function is the set of all possible input values (x-values) for which the function is defined. Since h(x) is a linear function, it is defined for all real numbers. Therefore, the domain is:
Domain: (-∞, ∞)
Range
The range of a function is the set of all possible output values (y-values). For linear functions, unless there’s a restriction, the range is also all real numbers. As x approaches both positive and negative infinity, h(x) will also approach infinity and negative infinity, respectively. Thus, the range is:
Range: (-∞, ∞)
Asymptote
Asymptotes are lines that a graph approaches but never touches. Linear functions do not have vertical or horizontal asymptotes because they extend infinitely in both directions. Therefore, h(x) = 0.5x + 9 has:
No asymptotes.
In summary:
- Domain: (-∞, ∞)
- Range: (-∞, ∞)
- Asymptotes: None