4. True/False. The domain and range of every cube and cube root function is always All Real Numbers. * O 7

8. Draw a picture of an even function and a picture of an odd function. You can use Desmos or draw by hand.

Use the graph of the function ffor the following 2) a) Find the domain and range of the function b) Evaluate f(2) 5-4-32

2. U = {11,22, 33, 44, 55}. V = {1,2,3, 4}. uRv if and only if u – v is diagram for R. Is Ra function? even. Draw an arrow

The function has a domain of all real numbers. 6-5 4 12 3 O True O False 5432

Mrs. Davis has 125 quarters to use at the laundromat. Each load of wash she does costs her $1.75. The total cost for her to do laundry is a function of the number of loads she does, x. Which is an appropriate domain for the function? A all integer values of x such that 0 < x < 72 B. all integer values of x such that 0 < x < 71 c. all integer values of x such that 0 < x < 18 D. all integer values of x such that 0 < x < 17

2. In each item below, you are given sets A and B, and a formula for a (non?)function f: A → B. In each case, determine whether or not the formula gives a well-defined function. Fully justify your answers. (a) A = Q = B, f(r) = a root in B of the polynomial X² - r (b) A = C = B, f(2)= a root in B of the polynomial X² – z (c) A = P(R) - {0}¹, B = R₁ ƒ(E) = the smallest element of E (d) A = P(R), B = R, ƒ(E) = the smallest element of E if E admits a smallest ele- ment, and f(E)= 0 otherwise A function f : A → B is injective (or one-to-one) if it satisfies the following condition: for all a₁, a2 € A, if f(a₁) = f(a₂), then a₁ = a₂; f is surjective (or onto) if f(A) = B, or, more explicitly, if for each b E B there exists a € A such that f(a) = b; f is bijective if f is both injective and surjective. Here are some examples. • The squaring function f : R → R given by f(x) = x² is not injective because f(-1) = 1 = f(1); f also fails to be surjective because -1 is not in the range of f. The…