Question 1: Expand or contract the expression using the properties of logarithms.
Question 2: Find the exact value without using a calculator. If this is not possible, state why not.
Question 3: Solve each equation algebraically.
Question 4: Use transformations to provide accurate graphs of the given functions. (Notice the similarities!) Describe the transformations in order and write out the transformations for the indicated point. Identify and graph any intercepts and asymptotes for each.
Question 5: The function is one-to-one. Find the inverse of each function and state the domain and range of f and f-1. Then, graph both f and f-1, identifying any intercepts and/or asymptotes.
Question 6: For each, provide a function having the given characteristics. Accurately graph each function, showing the characteristics.
- an exponential function with horizontal asymptote at y = -1 and y-intercept of (0, 1).
- a logarithmic function having vertical asymptote x = 4 and x-intercept of (5, 0)