College Alzebra Assignmment

Verbal 1. What is the difference between a relation and a function? 2. What is the difference between the input and the output of a function? 3. Why does the vertical line test tell us whether the graph of a relation represents a function? 4. How can you determine if a relation is a one-to-one function? 5. Why does the horizontal line test tell us whether the graph of a function is one-to-one? Algebraic For the following exercises, determine whether the relation represents a function. 6. {(a, b), (c, d), (a, c)} 7. {(a, b),(b, c),(c, c)} For the following exercises, determine whether the relation represents y as a function of x. 8. 5x + 2y = 10 9. y = x2 10. x = y 2 11. 3×2 + y = 14 12. 2x + y 2 = 6 13. y = −2×2 + 40x 14. y = __1 x 15. x = _ 3y + 5 7y − 1 16. x = √— 1 − y 2 17. y = ______ 3x + 5 7x − 1 18. x2 + y 2 = 9 19. 2xy = 1 20. x = y 3 21. y = x3 22. y = √— 1 − x2 23. x = ±√— 1 − y 24. y = ±√— 1 − x 25. y 2 = x2 26. y 3 = x2 For the following exercises, evaluate the function f at the indicated values f(−3), f(2), f(−a), −f(a), f(a + h). 27. f(x) = 2x − 5 28. f(x) = −5×2 + 2x − 1 29. f(x) = √— 2 − x + 5 30. f(x) = ______ 6x − 1 5x + 2 31. f(x) = ∣ x − 1∣ − ∣ x + 1∣ 32. Given the function g(x) = 5 − x2 , simplify g(x + h) − g(x) __ h , h ≠ 0 33. Given the function g(x) = x2 + 2x, simplify _ g(x) − g(a) x − a , x ≠ a 34. Given the function k(t) = 2t − 1: a. Evaluate k(2). b. Solve k(t) = 7. 35. Given the function f(x) = 8 − 3x: a. Evaluate f(−2). b. Solve f(x) = −1. 36. Given the function p(c) = c2 + c: a. Evaluate p(−3). b. Solve p(c) = 2. 37. Given the function f(x) = x 2 − 3x a. Evaluate f(5). b. Solve f(x) = 4 38. Given the function f(x) = √— x + 2: a. Evaluate f(7). b. Solve f(x) = 4 39. Consider the relationship 3r + 2t = 18. a. Write the relationship as a function r = f(t). b. Evaluate f(−3). c. Solve f(t) = 2.