which statements are true of the function $f(x)=3(2.5)^x$? check all that apply. the function is…

Explanation:

Step1: Identify function type

The function $f(x)=3(2.5)^x$ is in the form $y = ab^x$ where $a = 3$ and $b=2.5$, so it is exponential.

Step2: Find initial - value

When $x = 0$, $f(0)=3(2.5)^0=3\times1 = 3$, not $2.5$.

Step3: Analyze growth factor

For an exponential function $y = ab^x$, when $x$ increases by 1 unit, $y_1=ab^{x + 1}=ab^x\times b$. Here $b = 2.5$, so the function increases by a factor of $2.5$ for each unit increase in $x$.

Step4: Determine domain

For any real - valued $x$, the function $f(x)=3(2.5)^x$ is well - defined. So the domain is all real numbers.

Step5: Determine range

Since $(2.5)^x>0$ for all real $x$, then $f(x)=3(2.5)^x>0$. The range is all real numbers greater than $0$, not all real numbers greater than $3$.

Answer:

The function is exponential. The function increases by a factor of 2.5 for each unit increase in x. The domain of the function is all real numbers.