Question

hich 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

True:
- The function is exponential. (It has the form a·b^x.)
- The function increases by a factor of 2.5 for each unit increase in x. (Multiplying x by 1 multiplies f by 2.5.)
- The domain of the function is all real numbers. (Exponential functions are defined for all real x.)

False:
- The initial value of the function is 2.5. (f(0)=3·(2.5)^0=3.)
- The range of the function is all real numbers greater than 3. (Range is (0, ∞), since 3·(2.5)^x > 0 for all x and approaches 0 as x→−∞.)