Question

What are the domain and the range of this function? f(x) = log(x + 3) - 2

A. domain: (-3, ∞); range: (∞, 2)
B. domain: (3, ∞); range: (∞, 2)
C. domain: (3, ∞); range: (∞, ∞)
D. domain: (-3, ∞); range: (∞, ∞)

Answer 1

The domain is D. (-3, ∞) and the range is (-∞, ∞) for the given function f(x) = log(x + 3) - 2.

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, we have f(x) = log(x + 3) - 2.

Since we are taking the logarithm of (x + 3), the input value x + 3 must be positive. This means that the domain of the function is (-3, ∞), which represents all real numbers greater than -3.

The range of a function is the set of all possible output values (y-values) that the function can produce.

For the given function f(x) = log(x + 3) - 2, the logarithmic function will have a range of all real numbers.

However, since we are subtracting 2 from the function, the range will be shifted downward by 2. Therefore, the range of the function is (-∞, ∞), representing all real numbers.

Answer 2

the answer is c hope it helps