Yes, it is possible for a graph to have only one intercept. When a graph is a line that is parallel to either of the two axes, then the graph only has one intercept.
Work Step by Step
Vertical lines (except the y-axis) have x-intercepts but no y-intercepts. This is because vertical lines are parallel to the y-axis (and therefore will never touch nor cross the y-axis). Horizontal lines (except the x-axis) have y-intercepts but no x-intercepts. This is because horizontal lines are parallel to the x-axis (and therefore will never touch nor cross the x-axis). Thus, it is possible for a graph to have only one x-intercept.