Determine which of the following functions is NOT one-to-one. $y=|x+1|$ $y=\sqrt{x+1}$ $y=(x+1)^{3}$ $y=x+1$

Step 1 ：First, we need to understand that a function is one-to-one if it never takes on the same value twice. That is, every y value has a unique x value associated with it.

Step 2 ：For the function $y=|x+1|$, we can see that it is not one-to-one. For example, when $x=-2$ and $x=0$, the function takes on the same value of 1. So, this function is not one-to-one.

Step 3 ：For the function $y=\sqrt{x+1}$, it is one-to-one. The square root function is always one-to-one because for every y value, there is a unique x value.

Step 4 ：For the function $y=(x+1)^{3}$, it is one-to-one. The cubic function is always one-to-one because for every y value, there is a unique x value.

Step 5 ：For the function $y=x+1$, it is one-to-one. The linear function is always one-to-one because for every y value, there is a unique x value.

Step 6 ：So, the function that is NOT one-to-one is $y=|x+1|$.