The function f(x) = 3x + 5 is a linear function, which is a type of polynomial function. To determine the domain and range, let’s break it down:
Domain:
The domain of a function is the set of all possible input values (x-values) that will produce a valid output. For linear functions like f(x) = 3x + 5, there are no restrictions on the values of x. Therefore, the domain is all real numbers, which can be expressed in interval notation as:
Domain: (-∞, ∞)
Range:
The range of a function is the set of all possible output values (y-values). Since f(x) = 3x + 5 is also a linear function with a positive slope (3), as x takes on all real numbers, f(x) will also produce all real numbers. Hence, the range is also all real numbers:
Range: (-∞, ∞)
In summary, both the domain and range of the function f(x) = 3x + 5 are all real numbers, represented mathematically as:
Domain: (-∞, ∞)
Range: (-∞, ∞)