Question

An increasing linear function with independent variable x and dependent variable y approaches the point (−1, 1). If this function is defined only when x is greater than −1 and y is greater than 1, what are the domain and range of this function?

A. The domain is (−1,+[infinity]) and the range is (−1,+[infinity]).
B. The domain is (−1,+[infinity]) and the range is (1,+[infinity]).
C. The domain is (1,+[infinity]) and the range is (−1,+[infinity]).
D. The domain is (1,+[infinity]) and the range is (1,+[infinity]).

Answer 1

The domain and range of the increasing linear function defined only for x > -1 and y > 1 are (-1, infinity) and (1, infinity), respectively, corresponding to option B.

Step-by-step explanation:

The question relates to the domain and range of a linear function that is increasing and has certain restrictions on its x and y values. The domain of a function is the set of all possible input values (independent variable x), while the range is the set of all possible output values (dependent variable y).

The function in question is defined only for x values greater than -1 and y values greater than 1, which means the function does not exist at or below those values. Because the function is increasing, as x gets larger, y will also get larger. Therefore, the domain is all real numbers greater than -1, and the range is all real numbers greater than 1.

Thus, the correct answer to the question is: The domain is (-1,+infinity) and the range is (1,+infinity), which corresponds to option B.