By P.W. Michor
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76). y ( Horizontal shift (C) Amplitude (A) D DϪA ) y ϭ A sin 2 (x Ϫ C) ϩ D B DϩA This axis is the line y ϭ D. Vertical shift (D) This distance is the period (B). 76 The general sine curve y = A sin [s2p>Bdsx - Cd] + D , shown for A, B, C, and D positive (Example 2). 77 shows how to use such a function to represent temperature data. The data points in the figure are plots of the mean daily air temperatures for Fairbanks, Alaska, based on records of the National Weather Service from 1941 to 1970.
Y = 5x 6. a. y = 5x In Exercises 1–4, identify each function as a constant function, linear function, power function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. Remember that some functions can fall into more than one category. y g 5 b. gsxd = 2 x 1. a. ƒsxd = 7 - 3x x2 - 1 c. hsxd = 2 x + 1 2. a. Fstd = t 4 - t h x d. rsxd = 8 x 0 b. Gstd = 5t 3 7 d. Rszd = 2 z c. Hszd = 2z 3 + 1 3. a. y = c. y = x 5 3 + 2x x - 1 f b.
To shift the graph of y = ƒsxd to the left, add a positive constant to x. To shift the graph of y = ƒsxd to the right, add a negative constant to x. 54). 54). 55). 56). x 2 units Add a positive constant to x. 54 To shift the graph of ƒsxd = x 2 up (or down), we add positive (or negative) constants to the formula for ƒ (Example 4a and b). y Add a negative constant to x. 55 To shift the graph of y = x 2 to the left, we add a positive constant to x. To shift the graph to the right, we add a negative constant to x (Example 4c).