it crosses the point (-2, -4), which from there to the next crossing coordinate (-1, -2), it goes up +2 units on the y-axis and goes to the right on the x-axis +1 units
A counter-example would be the cubic polynomial y = x^3 which doesn't have a max or a min. The graph stretches forever in both directions (up and down) indicating that the range is the set of all real numbers.