# What is the domain and range of  y = 3 sqrt(x-4) + 2?

Jul 9, 2018

Domain is $x \ge 4 \mathmr{and} x \in \left[4 , \infty\right)$.
Range is $y \ge 2 \mathmr{and} y \in \left[2 , \infty\right)$.

#### Explanation:

 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 $x \ge 4 \mathmr{and} x \in \left[4 , \infty\right)$.

Range is possible output of $y \therefore y \ge 3 \cdot 0 + 2 \mathmr{and} y \ge 2$

Range is $y \ge 2 \mathmr{and} y \in \left[2 , \infty\right)$.

graph{3(x-4)^0.5+2 [-20, 20, -10, 10]}[Ans]