269 2.6 Graphs of Basic Functions The squaring function ƒ1x2 = x2 pairs each real number with its square. Its graph is a parabola. The point 10, 02 at which the graph changes from decreasing to increasing is the vertex of the parabola. See Figure 57. (For a parabola that opens downward, the vertex is the point at which the graph changes from increasing to decreasing.) LOOKING AHEAD TO CALCULUS Many calculus theorems apply only to continuous functions. Squaring Function ƒ1x2 =x 2 Domain: 1-∞, ∞2 Range: 30, ∞2 x y -2 4 -1 1 0 0 1 1 2 4 • ƒ1x2 = x2 decreases on the open interval 1-∞, 02 and increases on the open interval 10, ∞2. • It is continuous on its entire domain, 1-∞, ∞2. x y 0 f(x) = x2 4 3 2 1 1 2 –2 –1 −10 −10 10 10 f(x) = x2 Figure 57 The function ƒ1x2 = x3 is the cubing function. It pairs each real number with the cube of the number. See Figure 58. The point 10, 02 at which the graph changes from “opening downward” to “opening upward” is an inflection point. Cubing Function ƒ1x2 =x 3 Domain: 1-∞, ∞2 Range: 1-∞, ∞2 x y -2 -8 -1 -1 0 0 1 1 2 8 • ƒ1x2 = x3 increases on its entire domain, 1-∞, ∞2. • It is continuous on its entire domain, 1-∞, ∞2. x y 2 8 0 f(x) = x3 −10 −10 10 10 f(x) = x3 Figure 58
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