Solution
For this case we can do the following:
[tex]f(x)=2\sqrt[]{x+1}-3[/tex]
We can find:
f(0)= -1 , f(3) = 1
And we have:
[tex]\text{change}=\frac{1+1}{3-0}=\frac{2}{3}\text{ }[/tex]
For the new function g(x) we have:
[tex]\text{change}=\frac{g(3)-g(0)_{}_{}}{3-0}=\frac{-20+2}{3-0}=-6[/tex]
And for h(x) we have:
[tex]\text{change}=\frac{h(3)-h(0)}{3-0}=\frac{-3-0}{3-0}=-1[/tex]
For this case we can conclude that the greater rate of change needs to be g(x) no matter if is negative since we need to analyze the absolute value
