The function h(x) = 5x + 9 is a linear function, which means we can easily determine its domain, range, and asymptotes.
Domain:
The domain of a linear function is all real numbers. This means that you can input any value of x into the function without any restrictions. Mathematically, this can be expressed as:
Domain: (-∞, ∞)
Range:
Similarly, the range of a linear function that isn’t constrained (like h(x) = 5x + 9) is also all real numbers. As you plug in different values for x, the output of h(x) will cover all real numbers. Thus, we can say:
Range: (-∞, ∞)
Asymptote:
Linear functions do not have asymptotes. Asymptotes are typically associated with rational functions or functions that approach a particular line or value as x approaches infinity or negative infinity. Since h(x) = 5x + 9 is a straight line with a constant slope and does not approach any particular line or value, we can conclude:
No asymptotes.
In summary, for the function h(x) = 5x + 9:
- Domain: All real numbers (-∞, ∞)
- Range: All real numbers (-∞, ∞)
- Asymptote: None