sublimnes9

2022-08-18

What is the domain and range of $y=3\sqrt{x-4}+2$?

Nicholas Mathis

Expert

$y=3\sqrt{x-4}+2$; y is undefined , if under root function is
$<0\therefore x-4\ge 0\therefore x\ge 4$. Domain is possible input of x
Domain is $x\ge 4$ or $x\in \left[4,\mathrm{\infty }\right)$.
Range is possible output of $y\therefore y\ge 3\ast 0+2$ or $y\ge 2$
Range is $y\ge 2$ or $y\in \left[2,\mathrm{\infty }\right)$
graph{$3\left(x-4{\right)}^{0.5}+2\left[-20,20,-10,10\right]$}[Ans]

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