Question

What is the domain of the function y = sqrt x + 4?

Answer 1

Answer:

$[-4,\infty)$

Step-by-step explanation:

We are asked to find the domain of of the function $y=\sqrt{x+4}$.

We know that domain of a square root function is not defined for negative values, so we can set an inequality to find the domain of our given function as:

$x+4\geq 0$

$x+4-4\geq 0-4$

$x\geq -4$

Therefore, the domain of our given function is values of x greater than or equal to $-4$, that is $[-4,\infty)$

Answer 2

The domain is the set of numbers that the x value can be.
In an equation like $y=x$ the domain is all real numbers because x can be any number.

In the case of $y = \sqrt{x+4}$, any x value that is less than or equal to -4 will not work because you would be taking the square root of a negative number, which doesn't work unless you're graphing on a complex plane, which I assume you aren't.

Thus, the domain is $x \geq -4$
I hope that helps!