270 CHAPTER 2 Graphs and Functions The Square Root and Cube Root Functions The function ƒ1x2 = 2x is the square root function. It pairs each real number with its principal square root. See Figure 59. For the function value to be a real number, the domain must be restricted to 30, ∞2. Square Root Function ƒ1x2 =!x Domain: 30, ∞2 Range: 30, ∞2 x y 0 0 1 1 4 2 9 3 16 4 • ƒ1x2 = 2x increases on the open interval, 10, ∞2. • It is continuous on its entire domain, 30, ∞2. f(x) = !x x y 0 1 2 3 4 1 2 −10 −10 10 10 f(x) = !x Figure 59 The cube root function ƒ1x2 = 23 x pairs each real number with its cube root. See Figure 60. The cube root function differs from the square root function in that any real number has a real number cube root. Thus, the domain is 1-∞, ∞2. The Absolute Value Function The absolute value function, ƒ1x2 = 0 x 0 , which pairs every real number with its absolute value, is graphed in Figure 61 on the next page and is defined as follows. ƒ1x2 = ∣ x∣ = e x −x if x #0 if x *0 Absolute value function That is, we use 0 x 0 = x if x is positive or 0, and we use 0 x 0 = -x if x is negative. Cube Root Function ƒ1x2 = 3!x Domain: 1-∞, ∞2 Range: 1-∞, ∞2 x y -8 -2 -1 -1 0 0 1 1 8 2 • ƒ1x2 = 23 x increases on its entire domain, 1-∞, ∞2. • It is continuous on its entire domain, 1-∞, ∞2. x y 8 –8 2 0 f(x) = √x3 −10 −10 10 10 f(x) = !x 3 Figure 60
RkJQdWJsaXNoZXIy NjM5ODQ=