The table above gives values of a function g at selected values of x. Which of the following statements, if true, would be sufficient to conclude that there exists a number c in the interval [0,7] such that g(c)=50? x | 0 | 1 | 3 | 7 |
g(x) | 24 | 35 | 42 | 68 |

I. g is defined for all x in the intervals [0,7]
II. g is increasing for all x in the interval [0,7].
III. g is continuous for all x in the interval [0,7].