Honors Pre=Calculus Chapter 3 Review Graphing Exponential Functions→ Find the range, horizontal asymptote, and yintercept of the exponential function, and sketch the graph by hand. 1. f (x) = 4x 2. f (x) = ex + 2 3. f (x) = 3 − e−x Graphing Logarithmic Functions→ Find the domain, vertical asymptote, and xintercept of the logarithmic function, and sketch its graph by hand. 1. f (x) =− log 2x + 5 2. f (x) = log 2(x − 1) + 6 3. f (x) = log 5(x + 2) − 3 4. f (x) = log 5(x − 3) **Notice the differences in the graphs of logarithmic and exponential functions: i.e. domain vs. range, xintercept vs. yintercept. Why are there these differences? Rewriting Equations→ Write the logarithmic equation in exponential form or write the exponential equation in logarithmic form. 1. log 5125 = 3 2. 43 = 64 1 =− 2 3. log 10100 4. 12−1 = 121 Expanding Logarithmic Expressions→ Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. 1. log 55x2 2. ln x+3 xy 3. log 416xy2 5 4. lnxy√z Condensing Logarithmic Expressions→ Condense the expression to the logarithm of a single quantity. 1. log 29 + log 2x 2. log 6y − 2log 6z 1 ln(2x − 1) − 2ln(x + 1) 3. 4. 3[lnx − 2ln(x2 + 1)] + 2ln5 2 Finding the Exact Value→ Find the exact value of the following. 1. log 1/28 2. lne6 − 2lne4 Simplifying a Logarithm→ Use the properties of logarithms to rewrite and simplify the logarithmic expression. 1. ln√e5 2. log 3(92 ∙ 24) Solving an Exponential Equation→ Solve the exponential equation algebraically. Round your result to 3 decimal places. 1. 3e−5x = 132 2. 2ex−3 − 1 = 4 3. − ex/2 + 1 = 12 4. 2(12x) = 190 5. − 4(5x) =− 68 6. e2x − 6ex + 8 = 0 Solving a Logarithmic Equation→ Solve the logarithmic equation algebraically. Round your result to 3 decimal places. 1. ln3x = 6.4 2. lnx − ln5 = 2 3. ln√x + 1 = 2 4. log 4(x − 1) = log 4(x − 2) − log 4(x + 2) 5. log 10(1 − x) =− 1 6. log 10(− x − 4) = 2 Exponential Models→ 1. A total of $12,000 is invested at an annual interest rate of 3%. Find the balance after 4 years for each type of compunding. a. Quarterly b. Continuous 2. You deposit $7550 in an account that pays 6.9% interest, compounded continuously. How long will it take for the money to double?

© Copyright 2024 ExpyDoc