Question

Which statements are true of the function f(x) = 3(2.5)x? Check all that apply.

The function is exponential.
The initial value of the function is 2.5.
The function increases by a factor of 2.5 for each unit increase in x.
The domain of the function is all real numbers.
The range of the function is all real numbers greater than 3.

Answer 1

Assuming f(x) = 3(2.5)^x, the true statements are:

- The function is exponential. — True.
- The initial value of the function is 2.5. — False. f(0) = 3(2.5)^0 = 3, so the initial value is 3.
- The function increases by a factor of 2.5 for each unit increase in x. — True.
- The domain of the function is all real numbers. — True.
- The range of the function is all real numbers greater than 3. — False. The range is (0, ∞).