Question

How would the domain and range of the function y = 1/4x - 6 be determined? Explain.

A) The domain is all real numbers, and the range is all real numbers.
B) The domain is all real numbers except x = 0, and the range is all real numbers.
C) The domain is all real numbers, and the range is all real numbers except y = -6.
D) The domain is all real numbers except x = 4, and the range is all real numbers except y = -6.

Answer 1

The domain is all real numbers, and the range is all real numbers except y = -6.

Step-by-step explanation:

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In this case, the function is a linear function, and linear functions are defined for all real numbers. Therefore, the domain for the given function y = 1/4x - 6 is all real numbers.

The range of a function is the set of all possible output values (y-values) that the function can produce. In this case, the function is a linear function, and the range for linear functions is also all real numbers. However, there is a horizontal line at y = -6, which means that the function can never produce a y-value of -6. Therefore, the range for the given function is all real numbers except y = -6.