The function f(x) = 4x + 8 is a linear function, which can be analyzed to determine its domain and range.
Domain: The domain of a function refers to all the possible input values (x-values) that the function can accept. Since linear functions can take any real number as input, the domain of f(x) = 4x + 8 is:
- Domain: All real numbers, expressed in interval notation as (-∞, ∞).
Range: The range of a function refers to all the possible output values (y-values) that the function can produce. For the linear function f(x) = 4x + 8, as x takes on all real numbers, f(x) will also yield all real numbers. This is because linear functions do not have any restrictions on their outputs. Thus, the range is:
- Range: All real numbers, expressed in interval notation as (-∞, ∞).
In summary, the domain and range of the function f(x) = 4x + 8 are both all real numbers:
- Domain: (-∞, ∞)
- Range: (-∞, ∞)