Question

Describe the domain and range in (m(x) = |x+3|).

a) Domain: All real numbers; Range: (y ≥ 0)
b) Domain: All real numbers; Range: (y > 0)
c) Domain: All real numbers; Range: (y ≤ 0)
d) Domain: All real numbers; Range: (y < 0)

Answer 1

The domain of the function m(x) = |x+3| is all real numbers, and the range is all non-negative real numbers (y ≥ 0).

Step-by-step explanation:

For the function m(x) = |x+3|, the domain and range are as follows:

• Domain: The domain includes all possible values that x can take. Since there's no restriction on the values of x for the absolute value function, the domain is indeed all real numbers.
• Range: The range of an absolute value function is all non-negative values because the absolute value of any number is always zero or positive. Therefore, the function outputs y ≥ 0.

Based on these observations, the correct answer is:

a) Domain: All real numbers; Range: (y ≥ 0)