To find the domain and range of the function f(x) = 6x + 4, we’ll first look at the domain. The domain of a function refers to all the possible values of x that can be input into the function.
Since f(x) = 6x + 4 is a linear function (essentially a straight line), there are no restrictions on the values of x. You can plug any real number into this function and receive a corresponding output. Thus, the domain can be expressed as:
- Domain: All real numbers, or in interval notation, (-∞, ∞).
Next, let’s determine the range of the function. The range refers to all the possible output values (values of f(x)) that the function can produce. For the linear function f(x) = 6x + 4, as x takes on every real number, f(x) can also take on every real number due to the nature of linear equations. Therefore, the range is:
- Range: All real numbers, or in interval notation, (-∞, ∞).
In summary, both the domain and the range of the function f(x) = 6x + 4 are all real numbers. This is typical for linear functions, which do not have any restrictions on their inputs or outputs.