How do you find the domain and range of g(x)=3 sqrt(x+4)?

Dec 28, 2017

Domain: $x \ge - 4 \mathmr{and} x | \left[- 4 , \infty\right)$
Range: $g \left(x\right) \ge 0 \mathmr{and} g \left(x\right) | \left[0 , \infty\right)$

Explanation:

$g \left(x\right) = 3 \sqrt{x + 4}$ . For domain , under root is undefined for

any negative value. $\therefore x + 4 \ge 0 \mathmr{and} x \ge - 4$

Domain: $x \ge - 4 \mathmr{and} x | \left[- 4 , \infty\right)$

Range has no negative value , Range: $g \left(x\right) \ge 0 \mathmr{and} g \left(x\right) | \left[0 , \infty\right)$

graph{3*(x+4)^0.5 [-40, 40, -20, 20]} [Ans]