The graph is showing the behaviour of the function x^1/2, then, let's start with it:
[tex]f(x)=\sqrt[]{x}[/tex]
Now, we try to reach the given graph by multiplying and adding numbers to f(x). Firstly, the graph is always negative, so we multiply f(x) by -1.
[tex]g(x)=-\sqrt[]{x}[/tex]
Then, let's move the graph five units to the positive x position. To do so, we can add -5 to the x.
[tex]h(x)=-\sqrt[]{x-5}[/tex]
Finally, we need to multiply the function so that the curve opens at the rate of the given graph.
[tex]m(x)=-2\cdot\sqrt[]{x-5}[/tex]
As you can see, the graph is changing as we add or multiply by some factors. the red curve is pretty close to the given graph.
