6. Exponential & Logarithmic Functions

In Exercises 61–64, give the equation of each exponential function whose graph is shown.

Graph each function. Give the domain and range. See Example 3. ƒ(x) = -(1/3)^(x-2) + 2

In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = e^x and g(x) = 2e^(x/2)

In Exercises 1–4, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4^x, g(x) = 4^-x, h(x) = -4^(-x), r(x) = -4^(-x)+3 1.

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3^√5

Solve each equation. Round answers to the nearest hundredth as needed. (1/4)^x=64

In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^-0.95

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4^x

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-2)

In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (1/2)^x

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-5/2)

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3^x, g(x) = 3^(x-1), h(x) = 3^x - 1 ; f(x) = -3^x, G(x) = 3^(-x), H(x) = -3^(-x)

For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-1.68)