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 range of the function is all real numbers greater than 3 .

The function \( f(x)=3(2.5)^{x} \) is indeed an exponential function, characterized by a constant base raised to a variable exponent. This means that as \( x \) increases, the function grows rapidly. It's important to clarify that the initial value of the function \( f(0) = 3(2.5)^0 = 3 \), not 2.5, so that statement is false. Additionally, the function actually increases by a factor of 2.5 for each unit increase in \( x \) (which is true), but the range of the function is all real numbers greater than 0, not greater than 3. So make sure to keep an eye on those ranges!