To answer the question, let us plot the graphs of all the functions.
f(x):
[tex]f(x)=3|x+14|[/tex]
g(x):
[tex]g(x)=x^4+3x^2-14[/tex]
h(x):
[tex]h(x)=3^x+1[/tex]
i(x):
[tex]i(x)=\log _3(x+1)[/tex]
From the graphs shown above, it can be seen that the range of the function i(x) goes from -∞ to +∞. This is the function with the greatest negative range.
Therefore, the correct option is OPTION D
