According to the evidence in Example 4, it appears that (n) = (1 + 1) n never

According to the evidence in Example 4, it appears that ƒ(n) = (1 + 1)ⁿ never takes on a value greater than 3 for n > 0. Does this evidence prove that ƒ(n) ≤ 3 for n > 0?

Example No 4

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OF FIGURE 13 EXAMPLE 4 Sketch the graph of f(x) = 3 cos (2 (x + -)) over [0, 27]. Solution The graph is obtained by scaling and shifting the graph of y = cos x in three steps (Figure 13): horizontally by a factor of 2 . 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 + 1)) y = cos x y = cos (2(x + 5)) 14 IMA WA M 2π -1- Compress Expand y = cos 2x 2π x Shift left 7/2 units y = cos 2x y = cos (2(x + 7)) s(2(x + 7)) y = 3 cos -1 vertically by ➡>> a factor of 3 27