Explanation:
it is simple for such a line.
x goes to -infinity, and therefore y (or f(x)) also goes to -infinity.
x goes to +infinity, and therefore y (or f(x)) also goes to +infinity.
the difference between x and y values is just a constant factor (the slope). that constant factor becomes irrelevant, when the values approach infinity anyway. only the sign is relevant.
but in our case the slope is +1/+2 (the y value increases by +1 for every increase of x by +2).
so, the line (as we can see in the graph) is
y = 1/2 × x - 1
when x goes to +infinity, "-1" is irrelevant, and
1/2 × +infinity = +infinity.
when x goes to -infinity, again, "-1" is irrelevant, and
1/2 × -infinity = -infinity