the graph of f(x) = 1/2(2.5)^x and its reflection across the x - axis, g(x), are shown. what is the range of…

Explanation:

Step1: Recall reflection property

When a function $y = f(x)$ is reflected across the $x -$axis, the new function $g(x)=-f(x)$. Here $f(x)=\frac{1}{2}(2.5)^x>0$ for all real $x$. So $g(x)=-\frac{1}{2}(2.5)^x<0$ for all real $x$.

Step2: Determine the range

The function $g(x)$ can take any negative real - valued number, but never 0 or a positive number. So the range of $g(x)$ is all real numbers less than 0.

Answer:

all real numbers less than 0