Question

The graph of which function is decreasing over the interval

`( - 4, \infty`)
​

Answer 1

`-√(x + 4)`

Explanation:

1- It's known that shifting(called translation), reflection and rotation operations on th function would let us manipulate it as we like, and taking the square root function

`√(x)`

would let us to start graphing from the desired point in the xy-plane by using shifting operations on it.

2- Taking the minus of the square root function

`-√(x)`

would reflect the function over x-axis so the function would be decreasing from 0 to infinity.

3- Then, adding 4 to x in the square root

`-√(x+4)`

would make the domain of the function to start from
`x+4 > 0`or
`x > - 4` (by adding 4 to both sides).

4- Finally, the function of the domain (-4,
`\infty`) is

`-√(x+4)`.

I hope that I helped, and i'm sorry for any English mistakes(I'm not English speaker) .