Answer:
The correct option is 2. The range of g(x) is all real numbers less than 0.
Step-by-step explanation:
The given function is
\(f(x)=\frac{1}{2}(2.5)^x\)
If a graph reflected across x axis, then
\((x,y)\rightarrow(x,-y)\)
The function f(x) reflected across x-axis, so
\(g(x)=-f(x)\)
\(g(x)=-\frac{1}{2}(2.5)^x\)
It is an exponential function.
\(g(x)\rightarrow -\infty\text{ as }x\rightarrow \infty\)
\(g(x)\rightarrow 0\text{ as }x\rightarrow -\infty\)
Since the value of g(x) lies between \(-\infty\) and 0, therefore the range of g(x) is all real numbers less than 0. Option 2 is correct.
