Answer:
Range = [6, ∞)
Step-by-step explanation:
The range of a function is its output values (y-values).
One way to find the range of the given function is to determine the series of translations that have transformed the given function from the parent function.
Translations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function: [tex]f(x)=\sqrt{x}[/tex]
- Domain: [0, ∞)
- Range: [0, ∞)
Given function: [tex]f(x)=\sqrt{x-8}+6[/tex]
The parent function has been:
Translated 8 units right: [tex]f(x-8)=\sqrt{x-8}[/tex]
then translated 6 units up: [tex]f(x-8)+6=\sqrt{x-8}+6[/tex]
If the function has been translated 8 units right, the domain will be:
- Domain: [0 + 8, ∞) = [8, ∞)
Similarly, if the function has been translated 6 units up, the range will be:
- Range: [0 + 6, ∞) = [6, ∞)
