6. Exponential & Logarithmic Functions

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) = 3^x and g(x) = -3^x

Fill in the blank(s) to correctly complete each sentence. The graph of ƒ(x) = -(1/3)^x+4-5 is that of ƒ(x) = (1/3)^x reflected across the ______ -axis, translated to the left ______ units and down _______ units.

Solve each equation. See Examples 4–6. 4^x = 2

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

Begin by graphing f(x) = 2^x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn graphs. g(x) = 2^x+1

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

Use the compound interest formulas A = P (1+ r/n)^nt and A =Pe^rt to solve exercises 53-56. Round answers to the nearest cent. Suppose that you have \$12,000 to invest. Which investment yields the greater return over 3 years: 0.96% compounded monthly or 0.95% compounded continuously?

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