Question

H(x) = -(x + 5) - 7. What are the domain and range of the function?

A) Domain: All real numbers; Range: All real numbers
B) Domain: All real numbers; Range: Negative infinity to negative 12
C) Domain: All real numbers except x = -5; Range: Negative infinity to negative 7
D) Domain: All real numbers except x = -5; Range: All real numbers except y = -7

Answer 1

The domain of the function is all real numbers except x = -5, and the range is negative infinity to -12.

Step-by-step explanation:

The domain of a function represents the set of all possible inputs (x-values) for the function, while the range represents the set of all possible outputs (y-values). In this case, the function h(x) = -(x + 5) - 7 is a linear function, which means that the domain is all real numbers. However, there is one exception: x cannot be equal to -5 because it would result in division by zero. Therefore, the domain of the function is all real numbers except x = -5.

The range of the function can be determined by analyzing the behavior of the function. Since the function is a linear function with a negative slope, it decreases as x increases. The function reaches its minimum value at x = -5, which is equal to -12. Therefore, the range of the function is negative infinity to -12.