Polynomials are <em>closed</em> under addition and subtraction, which is fancy mathspeak that means that whenever we add or subtract two polynomials, we <em>always</em> get another polynomial. In that way, they behave a lot like the numbers you're probably already familiar with. Adding and subtracting:
Two integers gives you another integer
Two rational numbers gives you another rational number
The graph of g(x) would look the same as the given graph, EXCEPT that it'd be compressed by a factor of 1/3. Try graphing both f(x) and g(x) on your calculator and then comparing the 2 graphs.