Determine whether the following statements are true and give an explanation or counterexample.

a. All polynomials are rational functions, but not all rational functions are polynomials.

b. If f is a linear polynomial, then f ◦ f is a quadratic polynomial.

c. If f and g are polynomials, then the degrees of f ◦ g and g ◦ f are equal.

d. To graph g(x) = f(x + 2), shift the graph of f 2 units to the right.