Question

What is the domain and range of the function for (f(x) = 3333.22 times 33^x)?

a) Domain: All real numbers; Range: All real numbers
b) Domain: All real numbers; Range: (f(x) > 0)
c) Domain: (x > 0); Range: (f(x) > 0)
d) Domain: (x < 0); Range: (f(x) < 0)

Answer 1

The function f(x) = 3333.22 × 33^x is defined for all real numbers with a domain of all real numbers and a range where f(x) > 0. Thus, the correct answer is b) Domain: All real numbers; Range: (f(x) > 0).

Step-by-step explanation:

The domain of a function is the set of all possible inputs (x values) for which the function is defined, and the range is the set of all possible outputs (f(x) values). For the function f(x) = 3333.22 × 33^x, where x is a real number, we can determine the domain and range as follows:

• The base, 33, is positive, and the exponent x can be any real number, which means that f(x) will be defined for all real numbers. Thus, the domain is all real numbers.
• Since 33 to any real power is positive and it is multiplied by 3333.22, which is also positive, the function f(x) will always be positive. Therefore, the range is (f(x) > 0).

Based on this analysis, the correct answer is b) Domain: All real numbers; Range: (f(x) > 0).