The function you provided is a linear function of the form f(x) = mx + b, where m is the slope and b is the y-intercept. In your case, the slope m is 3, and the y-intercept b is 5.
Domain: In this case, the domain refers to all the possible values of x for which the function is defined. Since there are no restrictions on the value of x in a linear function, the domain of f(x) is all real numbers. We can express this formally as:
- Domain: (-∞, +∞)
Range: The range of a function is the set of all possible output values (f(x)) that the function can produce. For a linear function like f(x) = 3x + 5, as x takes on all real values, f(x) will also take on all real values. Hence, the range of f(x) is also all real numbers. This can be expressed as:
- Range: (-∞, +∞)
In summary, for the function f(x) = 3x + 5:
- Domain: (-∞, +∞)
- Range: (-∞, +∞)
Both the domain and range are all real numbers, which is typical for linear functions.