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 .

The function \( f(x)=3(2.5)^{x} \) is indeed an exponential function. Exponential functions are characterized by a constant base raised to a variable exponent; in this case, 2.5 is the base and \( x \) is the exponent. As \( x \) increases, the function rapidly grows, making it an exciting example of exponential growth! The initial value of the function is actually 3, not 2.5. This is because when \( x = 0 \), \( f(0) = 3(2.5)^{0} = 3(1) = 3 \). Also, while the function increases by a factor of 2.5 for each unit increase in \( x \), the function's growth means the domain is indeed all real numbers, while the range is actually all real numbers greater than 0! Keep those facts in mind for evaluations ahead!