Question

The graph of which function is decreasing over the intervald="TexFormula1" title="( - 4, \infty " alt="( - 4, \infty " align="absmiddle" class="latex-formula">)
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Answer 1

Answer:

$-\sqrt{x + 4}$

Step-by-step 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

$\sqrt{x}$

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

$-\sqrt{x}$

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

$-\sqrt{x+4}$

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

$-\sqrt{x+4}$.

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