Investigate the behavior of the function as n or x grows large by making a table of function values and plotting a graph (see Example 4). Describe the behavior in words.

ƒ(n) = 4n + 1/6n − 5

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-1- OF FIGURE 13 horizontally by a factor of 2 EXAMPLE 4 Sketch the graph of f(x) = 3 cos (2(x + 7)) over [0, 27]. Solution The graph is obtained by scaling and shifting the graph of y = cosx in three steps (Figure 13): -1 . . Compress horizontally by a factor of 2: Shift to the left 7/2 units: Expand vertically by a factor of 3: y = 3 cos (2(x + 2)) y = cos x y = cos 2x y = cos (2(x + 5) HE HAT WE MA 2π Compress Shift left Expand 7/2 units y = cos 2x 1- y = cos s(2(x + 7/-)) y = 3 cos (2 (²(x + 7/2)) vertically by →>> a factor of 3. -3-