Question

I will mark the answer with the best explanation as Brainliest!!! If anyone could help as soon as possible, I would greatly appreciate it!!!

Answer 1

Answer:

The second option is the correct answer.

Step-by-step explanation:

The range of a function of variable x means the set of all possible values of the function.

The function, is given by $f(x) = -1 -x, x < 0.\\f(x) = 1 + \sqrt{x} , x \geq 0.$.

$\frac{d f(x)}{dx} = -1, x < 0.\\\frac{d f(x)}{dx} = \frac{1}{2\sqrt{x} } , x \geq 0.$.

For x < 0, we can not find any maximum or minimum value. So, in this case we need to find the limits.

$\lim_{x \to -\infty} (-1 - x) = \infty.$.

Here, if you notice you will see as the function's value is - 1 - x, for x<0, the ultimate value of the function for all x<0 will be greater than - 1.

So, for x < 0 all the values of the function will be > -1.

For x > 0, $\lim_{x \to \infty} (1 + \sqrt{x} ) = \infty$.

For x = 0, the function's value will be 0.

The range of the function will be the all real numbers y > -1.