Precalculus - Heritage High School PreCal
Precalculus Name ___________________________
Transformations – HOMEWORK
Match the transformation of [pic]with the correct representation of the graph of h, where m is a constant and m > 0. Write the letter that it matches to in the blank. There are more choices than you need.
_______1. [pic] a. A horizontal shift of f, m units to the right
_______2. [pic] b. A horizontal shrink or stretch of f by m
_______3. [pic] c. A horizontal shift of f, m units to the left
_______4. [pic] d. A vertical shrink or stretch of f by m.
_______5. [pic] e. A vertical shift of f, m units upward
_______6. [pic] f. A reflection of f over the y-axis
g. A vertical shift of f, m units downward
h. A reflection of f over the x-axis
i. A vertical shrink or stretch of f by 1/m.
j. A horizontal shrink or stretch of f by 1/m.
Graph the transformations of the parent functions.
7) [pic] 8) [pic]
9) [pic] 10) [pic]
11) [pic] 12) [pic]
13) [pic]
14. Write an equation for the function that is described by the given characteristics.
____________________ a) The shape of[pic], but moved two units to the right and eight units downward.
____________________ b) The shape of[pic], but moved six units to the left and six units downward, and reflected in the y-axis.
____________________ c) The shape of[pic], but moved nine units downward and reflected in both the x-axis and the y-axis.
15. Determine whether the statement below is true or false. Justify your answer.
The graphs of [pic] and [pic] are identical.
16. Identify the parent function shown, then write an equation for the function shown in the graph.
a) b)
Parent Function ____________ Parent Function ____________
Equation with Transformations: Equation with Transformations:
_________________________ _________________________
c)
Parent Function ____________
Equation with Transformations:
_________________________
Precalculus Name___________________
3.1 WS Date_______Period________
____________ 1) A species of dolphins is decreasing at a rate of 3.1% per year. If there
are currently 20,000 dolphins, how many will there be in 30 years?
____________ 2) A home in Frisco is currently worth $300,000. If homes in Frisco are
appreciating at a rate of 4.7% % per year, when will the home be worth
$350,000?
____________ 3) If you buy a new car for $18,000 and cars depreciate at a rate of
about 7% per year, how much could you sell it for in 3 years?
____________ 4) If you bought your car 5 years ago for $15,000 and today you can sell
it for $7000, what was it’s rate of depreciation?
____________ 5) The half life of beryllium 11 is 13.8 seconds. If you start out with
50 grams, how much will be left in 3 minutes?
____________ 6) Carbon-14 decays with a halflife of about 5730 years. If archeologists
find a rock that had 10 grams of carbon-14, and it now has 7.2 grams
of carbon-14, how old is the rock?
7) If you get a total of $3000 as gifts when you graduate from high school and you put it
in a savings account that earns interest at a rate of 3.7% per year, how much would you
have in 4 years when you graduate from college if your interest is compounded…
____________ a) annually?
____________ b) quarterly?
____________ c) weekly?
____________ d) continuously?
____________ 8) If you invest $10,000 at a 2.6% interest rate compounded monthly,
how long would it take for your investment to grow to $15,000?
____________ 9) If you invested $100 in an account that compounded a 1.9% interest
rate continuously, how long would it take for you to have $1000?
____________ 10) If you find an account that has an interest rate of 2.8% compounded
quarterly, how long would it take for your money to triple?
Graph the following exponential functions. Label at least 2 points and the horizontal asymptote.
11) [pic] 12) [pic]
13) [pic] 14) [pic]
Precalculus
3.2 Log Functions WS NONCALCULATOR Name: _______________________
Write each equation in exponential form.
________ 1) [pic] ________ 2) [pic] ________ 3) [pic]
________ 4) [pic] ________ 5) [pic] ________ 6) [pic]
Find the value of each log.
________ 7) [pic] ________ 8) [pic] ________ 9) [pic]
________ 10) [pic] ________ 11) [pic] ________ 12) [pic]
________ 13) [pic] ________ 14) [pic] ________ 15) [pic]
________ 16) [pic] ________ 17) [pic] ________ 18) [pic]
________ 19) [pic] ________ 20) [pic] ________ 21) [pic]
________ 22) [pic] ________ 23) [pic] ________ 24) [pic]
Graph the following exponential functions. Label at least 2 points and any asymptotes.
25) [pic] 26) [pic]
27) [pic] 28) [pic]
29) [pic] 30) [pic]
31) [pic] 32) [pic]
33) [pic] hint: [pic] 34) [pic]
CALCULATOR PORTION
Evaluate each log using a calculator. Round answers to the nearest thousandths place.
________ 35) log3.1 ________ 36) log.76 ________ 37) log457
________ 38) ln4.7 ________ 39) ln239 ________ 40) ln.065
________ 41) log(-2.4) ________ 42) ln(-.57) ________ 43) log0
Precalculus
3.4 Solving Exponential & Log Equations WS Name: _____________________
Solve for x using a calculator. Round answers to the nearest thousandths place.
________ 1) logx = 0.7 ________ 2) logx = 3.6 ________ 3) logx = -.28
________ 4) lnx = 4.2 ________ 5) lnx = -1.5 ________ 6) lnx = -.57
Solve for x without using a calculator. Leave answers in terms of e when necessary.
________ 7) [pic] ________ 8) [pic] ________ 9) [pic]
________ 10) [pic] ________ 11) [pic]
________ 12) [pic] ________ 13) [pic]
________ 14) [pic] ________ 15) [pic]
________ 16) [pic] _________ 17) [pic]
_______ 18) [pic] _______ 19) [pic] _______ 20) [pic]
_______ 21) [pic] ________ 22) [pic]
Precalculus
3.5 Exponential & Logarithmic Models WS Name: _______________________
Find the exponential function passing through the given points. NO CALCULATOR!!!
____________ 1) (0,3) and (1,15) ____________ 2) f(0)=5 and f(4)=80
____________ 3) f(0)=64 and f(2)=4 ____________ 4) f(0)=80 and f(4)=5
____________ 5) f(1)=12 and f(2)=48 ____________ 6) f(1)=6 and f(3)=54
Solve the following word problems by taking the log of both sides of the equation.
7) There are currently 489 students at LHS. If that number is increasing at a rate of
1.8% per year. When will there be 650 students at LHS?
8) If you get $3000 for graduation gifts and invest it in an account that earns 2.4%
interest compounded quarterly, when will it grow to $5000?
9) The half life of the substance an ancient plate is made of is 432 years. If there
originally was 526 grams of the cup and now there is only 123 grams, how old is the
plate?
Solve the following word problems which involve logs.
10) The model for the Richter scale which rates the severity of earthquakes is
[pic] where [pic], I is the intensity of the quake and R is the Richter scale
value.
a) Find the intensity of a 5.1 quake. b) Find the intensity of a 8.3 quake.
c) If the intensity of a quake is 930,400,000 find the Richter scale value.
d) The intensity of a 4.1 on the Richter scale is _____ times more intense than a
4.0 on the Richter scale.
e) The intensity of a 6.0 on the Richter scale is _____ times more intense than a
5.0 on the Richter scale.
11) The acidity (or pH) model given by [pic] is a measure of the hydrogen ion
concentration [pic] measured in moles of hydrogen per liter of solution.
a) Find the pH of a solution with [pic] moles per liter.
b) How many moles per liter are in a solution with a pH of 2.3?
12) The level of sound [pic] (in decibels) with an intensity of I is given by [pic]
where [pic] is an intensity of [pic] watts per square meter. Find the sound level [pic] for
the following situations:
a) [pic] watts/m[pic] (quiet room)
b) [pic] watts/m[pic] (slamming door)
c) [pic] watts/m[pic] (threshold of pain in ears)
Write the first five terms of the sequence. (Assume that n begins with 1.)
2) [pic]
4) [pic]
6) [pic]
8) [pic]
12) [pic]
Find the indicated term of the sequence.
24) [pic]; [pic]
Write an expression for the nth term of the sequence. (Assume that n begins with 1.)
38) 3, 7, 11, 15, 19, … 40) 2, -4, 6, -8, 10, … 42) [pic], [pic], [pic], [pic], …
Write the first five terms of the recursive sequence.
52) [pic]; [pic]
54) [pic]; [pic]
Write the first five terms of the recursive sequence, and use the pattern to write the explicit formula of the sequence. (Assume that n begins with 1.)
56) [pic]; [pic]
58) [pic]; [pic]
Write the first five terms of the sequence.
60) [pic]
62) [pic]
Simplify the factorial expression.
66) [pic] 68) [pic]
Find the sum.
74) [pic]
76) [pic]
78) [pic]
9.2 WS CALCULATOR Name___________________
Precalculus Date_________Period______
Determine whether the sequence is arithmetic. If so, find the common difference.
1. [pic] 2. [pic] 3. [pic]
Write the first five terms of the sequence. Determine whether the sequence is arithmetic. If so, find the common difference. (Assume that n begins with 1).
4. [pic] 5. [pic] 6. [pic]
7. [pic]
Find a formula for [pic]for the arithmetic sequence.
8. [pic], [pic] 9. [pic],[pic] 10. [pic]
11. [pic],[pic] 12. [pic], [pic]
Write the first five terms of the arithmetic sequence.
13. [pic], [pic]
Write the first five terms of the arithmetic sequence. Find the common difference and write the nth term of the sequence as a function of n.
14. [pic],[pic] 15. [pic], [pic]
The first two terms of the arithmetic sequence are given. Find the missing term.
16. [pic],[pic], [pic]
Find the indicated nth partial sum of the arithmetic sequence.
17. [pic][pic] 18. [pic][pic]
19. [pic][pic]
Find the partial sum.
20. [pic] 21. [pic]
Determine whether the sequence is geometric. If so, determine the common ratio.
2) 3, 12, 48, 192, … 4) 36, 27, 18, 9, … 6) 5, 1, 0.2, 0.04, …
Write the first five terms of the geometric sequence. (Assume that n begins with 1.)
12) a1=6, r=2 16) a1=1, r=[pic]
____, ____, ____, ____, ____, … ____, ____, ____, ____, ____, …
Write the first five terms of the geometric sequence. (Assume that n begins with 1.) Determine the common ratio, and write an equation for the nth term of the sequence.
22) a1=81, ak+1=[pic](ak) ____, ____, ____, ____, ____, … r =___
an=__________________
24) a1=5, ak+1= -2(ak) ____, ____, ____, ____, ____, … r =___
an=__________________
Write an equation for the nth term of the geometric sequence. Then find the indicated term.
28) a1=5, r=[pic], n=8 an=____________________
a8=_________
30) a1=64, r=[pic], n=10 an=____________________
a10=_________
36) 7th term: 3, 36, 432, … an=____________________
a7=_________
38) 22nd term: 4, 8, 16, … an=____________________
a22=_________
40) 1st term: a2=3, a5=[pic] an=____________________
a1=_________
42) 7th term: a3=[pic], a5=[pic] an=____________________
a7=_________
Find the sum of the finite geometric sequence.
54) [pic] 56) [pic]
58) [pic] 60) [pic]
-----------------------
Section 9.1 Sequences and Series – WS Name: ______________________
(Textbook Page 649) Date: ____________ Period: ____
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
[pic]
[pic]
[pic]
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
[pic]
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
[pic]
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
|a1 |a2 |a3 |a4 |a5 |
| | | | | |
Section 9.3 Geometric Sequences and Series – WS Name: _______________________
(Textbook Page 669) Date: ____________ Period: ____
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