\f\fThe statement is true. Continuous functions have graphs that are continuous and without jumps. Uniformly continuous functions are the same, but have an added condition that there should not be a condition that the value of the function changes .more and more rapidly as we move towards the edge of the domain In a closed domain, like the closed region R given in the question, if the function f is continuous, it will have no sudden increase in value at the edges. Thus, any continuous function in a closed region is uniformly continuous. Only functions where at least once side of the interval is open, can have the possibility of being continuous but not .uniformly continuous \f\fThe statement is true. Continuous functions have graphs that are continuous and without jumps. Uniformly continuous functions are the same, but have an added condition that there should not be a condition that the value of the function changes .more and more rapidly as we move towards the edge of the domain In a closed domain, like the closed region R given in the question, if the function f is continuous, it will have no sudden increase in value at the edges. Thus, any continuous function in a closed region is uniformly continuous. Only functions where at least once side of the interval is open, can have the possibility of being continuous but not .uniformly continuous \f