Answer:
[tex]\mathrm{Domain\:of\:}\:0.5^x-9\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Range\:of\:}0.5^x-9:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>-9\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-9,\:\infty \:\right)\end{bmatrix}\\\\\mathrm{Asymptotes\:of}\:0.5^x-9:\quad \mathrm{Horizontal}:\:y=-9[/tex]
Step-by-step explanation:
Domain:
The function has no undefined points nor domain constraints. Therefore, the domain is
[tex]...-\infty \:<x<\infty \:[/tex]
Definition: The domain of a function is the set of input or argument values for which the function is real and defined.
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Range:
[tex]\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k\\k=-9[/tex]
[tex]f\left(x\right)>-9[/tex]
Definition: The set of values of the dependent variable for which a function is defined.
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Asymptotes:
[tex]\mathrm{Vertical\:asymptotes\:of\:}0.5^x-9:\quad \mathrm{None}\\\mathrm{Horizontal\:Asymptotes\:of\:}0.5^x-9:\quad y=-9\\\mathrm{Horizontal}:\:y=-9x^{2}[/tex]
