Solutions to the Odd Exercises for Functions 1. A function is a rule that assigns to each element of a domain set to a unique element of a range set. For exercises 3 through 6 answer either "True" or "False" and explain how you arrived at your conclusion. 3. The graph of a function can never have more than one y-intercept. True, since if it had more than 1 y-intercept, then the x-value 0 would be assigned to more than one y-value. 5. Every line is the graph of a function. False, vertical lines are not graphs of functions. For exercises 7 - 10, a relation is given in the form of ordered pairs. Determine the domain, the range, state whether the relation is a function. 7. (1,2), (2,3), (3,4), (4,5), (7,7) Domain = {1,2,3,4,7} Range = {2,3,4,5,7} This relation is a function. 9. (0,2), (1,6), (1,5), (9,12), (10,11) Domain = {0,1,9,10} Range = {2,5,6,11,12} This relation is not a function since the value 1 gets assigned to two numbers.
For exercises 11 through 14, graphs are given. Determine whether the graph is a function and explain your reasoning. 11. 13.
For exercises 15 - 18, determine the domain and range and state whether the relation described is a function. 15. Every person is assigned to his or her biological mother. Domain: All people, Range: All mothers. This is a function. 17. Every word is assigned that are generated during a Google search. Domain: All words, Range: All URL's. This is not a function. For exercises 19 - 28, let f(x) = 3x - 4 and g(x) = x2 + x and h(x) = 3. Find the indicated value. 19. f(2) 2 21. h(-4) 12 23. g(x + 1) x2 + 3x + 1 25. (f - g)(4) -12 27. (f / g )(2) 1/3 29. g(x + 1) - g(x) 2x + 2 31. (g h)(5) 90 For exercises 32 through 39, use the graphs shown below to approximate the indicated value.
33. g(-3) 3 35. g(8) 1 37. (f - g)(-5) 0 39. (f / g)(6) -2 Find the domain of the functions given in exercises 40 - 43. 41. f(x) = x2 + x - 2 All real numbers 43.
3x
- 4 All real numbers except for x = 1/5 For exercises 44 - 47 use the given graphs to find the domain and the range. 45.
47.
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