Suppose that $g$ is the function given by the graph below. Use the graph to fill in the blanks in the following sentences.

As $x$ gets closer and closer to (but stays less than) $1$, $g(x)$ gets as close as we want to .

As $x$ gets closer and closer to (but stays greater than) $1$, $g(x)$ gets as close as we want to .

As $x$ gets closer and closer (but not equal) to $1$, does $g(x)$ get as close as we want to a single value? If such a value exists, enter it. If no such value exists, enter DNE.
$x =$ .