# How do you find the domain and range of  sqrt(t+7)?

Feb 16, 2017

$D : \left[- 7 , \infty\right)$
$R : \left[0 , \infty\right)$

#### Explanation:

a square root can never be negative inside, it would mean that there are no real numbers, no real solution (unless we're going into imaginary numbers)

so set the this rational expression to 0
$t + 7 \ge 0$
you put $\ge$ because we know that the end behavior of root functions look like this:

graph: $y = \sqrt{t}$
graph{y=sqrtx [-10, 10, -5, 5]}

$t \ge - 7$,
so $D : \left[- 7 , \infty\right)$

and $R : \left[0 , \infty\right)$ because we know that the end behavior of the root function looks like that

note: if the equation were $y = \sqrt{t + 7} + 1$ then the range would be $R : \left[1 , \infty\right)$

graph: $y = \sqrt{t + 7}$
graph{y = sqrt(x + 7) [-10, 10, -5, 5]}