Chapter 1.2, Problem 53E

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

1. a. All polynomials are rational functions, but not all rational functions are polynomials.
2. b. If f is a linear polynomial, then f ∘ f is a quadratic polynomial.
3. c. If f and g are polynomials, then the degrees of f ∘ g and g ∘ f are equal.
4. d. To graph g(x) = f(x + 2), shift the graph of f 2 units to the right.