Answer:
The range is
B. [tex]y\:<\:0[/tex]
Step-by-step explanation:
The given function is
[tex]f(x)=-2(0.5)^x[/tex]
Let [tex]y=-2(0.5)^x[/tex]
The range refers to y-values for which x is defined.
We solve for x to get;
[tex]-\frac{y}{2} =0.5^x[/tex]
[tex]\log(-\frac{y}{2}) =\log(0.5)^x[/tex]
[tex]\log(-\frac{y}{2}) =x\log(0.5)[/tex]
[tex]x=\frac{\log(-\frac{y}{2}) }{\log(0.5)}[/tex]
x is defined for;
[tex]-\frac{y}{2}\:>\:0[/tex]
Multiply by -2 and reverse the inequality sign.
[tex]\implies y\:<\:0[/tex]
