Question

Very straightforward question that can easily be answered by plotting out every answer in a graphing calculator, but I don't have a graphing calculator !! Please help, thanks!

Answer 1

Explanation

Given the function

$\begin{gathered} f(x)=\sqrt{x} \\ f(x)=\sqrt{x+1} \\ f(x)=\sqrt{10x+1} \end{gathered}$

We can find which one of the functions grows the fastest as x goes to infinity using the graphing calculator.

The blue line above represents

$f(x)=\sqrt{10x+1}$

Clearly from its nature, we can state that it grows the fastest as x goes to infinity.

Answer:

$f(x)=\sqrt{10x+1}$