Each function f is defined as f :R +R. Prove why each of the functions is one to one or not c one. (a) f(z) = , z + 3. (b) f(z) = for all real mumbers.

= mx + b. 4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) x + 2, and h(x) A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (−1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. =

Evaluate the piecewise function at the given value of the independent variable. ={x - f(x) = [x - 1 1-(x - 1) ifx s-3 if x>-3. f(-5) А) 6 B) -6 17 D) -5 C.

Consider the functions f: [7] to [9].  How many of these functions have a range of {5,6}?