Final answer:
The domain of the function m(h) = 12h + 20 is all real numbers because there are no restrictions on h. The range is all values of m(h) that are greater than or equal to 20, because this is the minimum value m(h) can take when h is zero.
Step-by-step explanation:
To find the domain and range of the equation m(h) = 12h + 20, we need to examine what values the variable h can take on (the domain) and what values the function m(h) can produce (the range).
Since there are no restrictions given on h, it can be any real number. Therefore, the domain is all real numbers. For the range, we look at the smallest and largest values m(h) can take. Since h can be any real number, the smallest m(h) can be is when h is at its smallest, which is negative infinity. However, due to the nature of the linear function, as h goes to negative infinity, the value of m(h) also goes to negative infinity, which means there is technically no minimum. But we typically look at the intercept where h = 0, then the function gives m(0) = 12(0) + 20 = 20. Any value of h greater than zero gives a value of m(h) greater than 20. Thus, the range is m ≥ 20.
The correct answer to the question is c) Domain: All real numbers; Range: m ≥ 20.