```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? ```