Answer:
B. I, II, and III
Explanation:
A function is continuous if it is defined everywhere and its graph can be drawn without lifting the pencil. That is, at every point, the limit from the left and the limit from the right must equal each other and the function definition at the point.
Looking at choices
All polynomial functions with real coefficients are continuous everywhere. (Choices I and II.) They have no discontinuities.
Rational functions will have a discontinuity wherever the denominator is zero. Here, the one rational function has a denominator of x^2+1, which is always positive (never zero). The given rational function is continuous everywhere (Choice III.)
All of the functions in the problem statement are continuous: I, II, and III.