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