Question 6.10.11: Graphing an Exponential Function with a Base Greater Than 1 ......

a) Substitute values for x and find the corresponding values of y. The graph is shown in Fig. 6.49 on page 380.

y = 2^x

x = -3,     y = 2^{-3} = \frac{1}{2³} = \frac{1}{8}

x = -2,     y = 2^{-2} = \frac{1}{2²} = \frac{1}{4}

x = -1,     y = 2^{-1} = \frac{1}{2¹} = \frac{1}{2}

x = 0,     y = 2^0 = 1

x = 1,     y = 2¹ = 2

x = 2,     y = 2² = 4

x = 3,     y = 2³ = 8

b) The domain is all real numbers, \mathbb{R}. The range is y > 0. Note that y can never have a value of 0.