1. Let f(x) be a function about which we know nothing. Find which of the following statements is false.

A. g(x) = f(x) + f(-x) is an even function

B. g(x) = f(x) - f(-x) is an odd function

C. g(x) = f(|x|) is an even function

D. g(x) = f(-|x|) is an odd function

E.. g(x) = f(x^2) is an even function

2. Assume that f(x) and g(x) are both polynomial functions. Which one of the following statements is necessarily true?

A. If the degree of f(x) is bigger than the degree of g(x), then f(x) has more distinct solutions than g(x).

B. If the degree of f(x) is bigger than the degree of g(x), then f(x) has more distinct solutions (counting multiplicities) than g(x).

C. If the degree of f(x) is even, and the degree of g(x) is odd, then their graphs are going to cross at least once.

D. If the degrees of both f(x) and g(x) are even, then the degree of f(x) + g(x) is also even.

E. If the degrees of both f(x) and g(x) are even, then the degree of f(x)g(x) is also even.

3. Assume that f(x) is a polynomial function of degree 3, and the leading coefficient is 1. Assume moreover, that f(x) has 2 distinct solutions. Then:

A. No such function is possible.

B. There is a unique such function.

C. There are 2 different such functions.

D. There are 3 different such functions.

E. There are 4 different such functions.