[tex]g(x)=\dfrac{a}{x}\\\\\text{The domain:}\\\\x\neq0\\\\\boxed{D=\{x\ |\ x\in\mathbb{R},\ x\neq0\}}\\\\\text{The range}:\ \boxed{R=\{y\ |\ y\in\mathbb{R},\ y\neq0\}}.[/tex]
Function Transformations
f(x) + n - translate the graph of f(x) n units up
f(x) - n - translate the graph of f(x) n units down
f(x + n) - translate the graph of f(x) n units left
f(x - n) - translate the graph of f(x) n units right
[tex]g(x)=\dfrac{2}{x}\\\\g(x-3)=\dfrac{2}{x-3}\\\\g(x-3)+4=\dfrac{2}{x-3}+4\\\\f(x)=g(x-3)+4[/tex]
translate the graph of [tex]g(x)=\dfrac{2}{x}[/tex] 3 units right and 4 units up.
Therefore the domain is:
[tex]\{x\ |\ x\in\mathbb{R},\ x\neq0+3\}=\{x\ |\ x\in\mathbb{R},\ x\neq3\}[/tex]
and the range is:
[tex]\{y\ |\ y\in\mathbb{R},\ y\neq0+4\}=\{y\ |\ y\in\mathbb{R},\ y\neq4\}[/tex]
Answer:
A. The domain is {x |x ∈ R, x ≠ 3}.
The range is {f(x) | f(x) ∈ R, f(x) ≠ 4}.
