# Download Calculus by Stanley I Grossman PDF By Stanley I Grossman

1,178 pages plus Appendixes of 146 pages

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Example text

I h l·UNC T I 35 1 . 6 FUNCTIONS Let us return to the equation of a straight line. For example, if y = 3x + 5, then the line can be thought of as the set of all ordered pairs (or points) (x, y) such that y = 3x + 5 . The important fact here is that for every real number x there is a unique real number y such that y = 3x + 5 and the ordered pair (x, y) is on the line. We generalize this idea in the following definition. FUNCTION Let X and Y be sets of real numbers. A function f is a rule that assigns to each number x in X a single number f(x) in Y.

28. 30. 32. 34. 36. •38. •40 . •42. v = h(u) = l u - 21 1 y = f(x) = Ix + 21 x, x 2: 1 y = 1, x<1 x 2 + 3x y = x +3 1 y = -� + 2 vx 1 + 3 y= x - 1 x Y = x + 1 2x + 3 y = 3x + 4 2y = V x_-+ 2--,,_ x""'" _ -,3_ 25. '-=-1 27. y = f(x) = JX1 { 29• y = +-- 35. y = 44. y = 3x2 - 5, x 2: 2 1 x +1 31. y = 33. y = •37 Y = • •39. y = •41 y = · •43. y = 45. y = {x,- x , {xx3, 1 x 2: 0 x <0 x >0 < 0 xx5 + 5x2 x2 1 + 3 x2 + 1 1 1 + x2 + x4 + x6 x2 x2 + 3 x" n an integer 2: 1 x" + l ' 'V,_ x2 = -_,, x_-+ 2-,- 3_ 1 -, x < 3 x 2 I -- •46.

Let y (i) (ii) (iii) (iv) 1)2 = f(x). To obtain the graph of y = f(x) + e, shift the graph of y = f(x) up e units if e 2: 0 and down l ei units if e < 0. To obtain the graph of y = f(x - e), shift the graph of y = f(x) to the right e units if e > 0 and to the left lei units if c < 0. To obtain the graph of y = f(x), reflect the graph of y = f(x) through the - x-axis. To obtain the graph of y = y-axis. f( -x), reflect the graph of y = The graph of y = Vx is given in Figure 2a. Then using the above rules, the graphs of Vx + 3, Vx - 2, �, \IX+3 = Vx - ( - 3), - Vx , and v=i are given in the other parts of Figure 2.