Explanation:
The question wants us to determine the range of the given function
[tex]f(x)=\frac{2x+4}{x-2}[/tex]
The graph below also helps us in answering this question
The range of a function is defined as
[tex]\mathrm{The\: set\: of\: values\: of\: the\: dependent\: variable\: for\: which\: a\: function\: is\: defined}[/tex]
The solution to the function is given by
[tex]\begin{bmatrix}\mathrm{Solution\colon}\: & \: f\mleft(x\mright)<2\quad \mathrm{or}\quad \: f\mleft(x\mright)>2\: \\ \: \mathrm{Interval\: Notation\colon} & \: \mleft(-\infty\: ,\: 2\mright)\cup\mleft(2,\: \infty\: \mright)\end{bmatrix}[/tex]
Therefore, the range is all real numbers except y = 2
