Chapter 1 - Worksheet 3 - NEW FUNCTIONS FROM OLD
NAME_
1. Give values so that the table represents an invertible function
m
f (m)
1
2
3
0.0 _ _
9
_
_
Any numbers except 0.09, 7.8 and 9.4
4
5
7.80 9.40
2. For what values of A and K will S (t ) = At 3 K be
Chapter 1 Worksheet 4 - LOGARITHMS
NAME_
1. Calculate the following. Whenever possible give the exact value. If the value does not exist, state DNE.
A. log ( 1.035 )
0.01494
1
B. log 4
64
-3
C. log 2 ( 4 )
DNE
D. ln ( e )
E. log 9 ( 3)
On some of these
Chapter 1 - Worksheet 2 - EXPONENTIAL FUNCTIONS
Place answers on this sheet. Show work on your own paper.
NAME_
1. Determine which table illustrates an exponential function and which one illustrates a linear function. Find
formulas for these two functions
MATH 122A
FINAL EXAM STUDY GUIDE ANSWERS
(Fall 2016 Spring 2017)
( ,
1. a)
d)
20 20,
( , 4 ) ( 4, )
2. a) Ax + By =
0 or y =
)
b)
e)
A
x
B
( , 2 ) ( 2, )
( 0, )
b) y=
3. a) 90 minutes after leaving Phoenix.
c)
( , )
B
( x 2) 1
A
b) 80 miles per hour
(2
WS5-TRIGONOMETRY PART 1
NAME_
1. Sketch the angle in standard position. Then find the exact values for cos and tan .
A.
7
3
B.
5
4
C.
2. In each case, determine the quadrant(s) for angle T.
A. sin T 0 and cos T 0
D.
B. cos T 0 and tan T 0
C. sec T 0 a
WS4-LOGARITHMS
NAME_ 154
Sec # _
1. Calculate the following. Whenever possible give the exact value. If an exact value cant be given, round to 4
decimal places. If the value does not exist, state DNE.
A. log (1.035 )
1
B. log 4
64
C. log 2 ( 4 )
D. l
PREPARING FOR MATH 122A
Functions for Calculus, Math 122A, is meant to further develop what students with a strong background in PreCalculus can do with the tools that they have already learned. The problems below are
those we feel students should be able
WS7-POLYNOMIAL AND RATIONAL
NAME_
(There are 4 pages)
SEC # _
1. Suppose a polynomial function has degree n and leading coefficient c.
Complete the following statements.
154
A. The number of turning points is at most_.
B. If n is odd and c>0, then y appro
WS1-FUNCTIONS
NAME_154
SHOW WORK AND ALWAYS USE PROPER NOTATION.
SEC #_
1. The relationship between the tuition, T (in dollars), and the number of credits, c, at a particular college is
given by
0c6
100 + 120c
T (c ) =
800 + 120(c 6) 6 < c 18
A. What is
WS8-LIMITS AND CONTINUITY
NAME_
SEC #_
1. Generate a table of values to find each of these limits. Include the table with at least 6 sets of values,
which clearly indicates your conclusion.
A. lim(1 + x)1 x
x 0
D. lim
t 1
1 t
B. lim
sin(2 )
0
C. lim
y
y
WS3-NEW FUNCTIONS FROM OLD
NAME_144
1. Draw an invertible function. State at least 2 characteristics of an invertible function.
2. For what values of A and K will S (t ) At 3 K be an invertible function?
Your answer should be based on transformation of 3
MATH 122A
FINAL EXAM STUDY GUIDE
(Fall 2016-Spring 2017)
The questions on the Math 122A final exam have a multiple choice format while the
questions in this study guide are not multiple-choice in order to encourage you to solve the
problems completely. Th
Chapter 1 - Worksheet 1 - FUNCTIONS
NAME KEY
144
1. The relationship between the tuition, T (in dollars), and the number of credits, c, at a particular college is
given by
0c6
100 + 120c
T (c ) =
800 + 120(c 6) 6 < c 18
A. What is the tuition for 7 credi
Name
Homework 3
Section 1.3
1. (2ea) Use the functions below to compute the following quantities. Show some work!
8
f (x) = x2 2
y
6
4
2x
g(x) =
x3
2
x
x
2
1
h(x)
3
2
0 1 2 3
1 3 4 5
8 6 4 2
2
4
2
4
graph of k(x)
S17
a) (f h)(2)
b) k 1 (3)
c) (h h)(1)
d)
Name
Homework 4
Section 1.3
1. (6) Given that
S17
g(x) = x2 +x, compute and simplify the expression
g(x + h) g(x h)
2h
2. (3ea) Determine functions
functions
(a)
h(x).
Do not use
f (x) and g(x) so that f (g(x) = h(x)
f (x) = x or g(x) = x.
h(x) = (x2 + 1)
Name
Homework 5
Section 1.4
1. (4) A colony of bacteria grows in a controlled environment according to the function
Q(t) = 12000(1.015)t , where t is measured in weeks.
(a) What is the weekly growth rate (as a percentage) of the bacteria population?
(b) W
Name
Homework 2
Section 1.2
1. (5) Consider a function, f (x), whose graph passes through the point (1, 9) and for
which f (3) = 49. Determine an exponential function which satises these properties.
2. (2ea) A certain radioactive substance decays at a con
Name
Homework 6
Sections 1.5
1. (5) Find a solution to the following equation:
3 = 8 cos(2x + 1) + 7
2. (2,4) A population of crickets oscillates sinusoidally over the course of one year between
a low of 500 on April 1 and a high of 30,500 on October 1.
(
Name
Homework 7
Section 1.6
1. (2ea) For each of the polynomial functions graphed below, determine whether the
leading coecient is positive or negative, and the lowest possible degree.
The leading coecient is
y
Positive
a)
x
Negative
The lowest possible d
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WS2-EXPONENTIAL FUNCTIONS
NAME_154
Sec # _
1. Determine which table illustrates an exponential function and which one illustrates a linear function. Find the
exact formula for these two functions. Your work must verify that the function is linear (three s
WS6-TRIGONOMETRY PART 2
NAME_
x
1. Find the exact value for csc tan 1
. Your answer will be in terms of x.
2
Hint: Make a right triangle and fill in the missing side.
2. Find exact value for each:
A. cos 1 (1) =
1
B. sin 1 =
2
3. Solve the follo
MATH 122A
FINAL EXAM STUDY GUIDE ANSWERS
(Fall 2012)
(
)
1. a) t 20 or t 20 . You can also write this as , 20 20, .
b) y 2 . You can also write this as ( , 2 ) ( 2, ) .
2. a)
b)
h
c)
h
t
h
t
t
(Be sure to label your axes.)
3. a) L = kS 2 A
b) If the speed
Chapter 1 - Worksheet 1 - FUNCTIONS
NAME_
1. As you travel at a fairly constant speed from Tucson to Bisbee (94 miles), you pass through Benson.
Benson is 40 miles from Tucson. Sketch graphs to represent the functions below. Label your graphs.
Hint: See a
Chapter 1 - Worksheet 5 - TRIGONOMETRY PART 1
NAME_
1. Consider the transformation y = A sin( Bx + C ) + D where A, B, C , and D are positive constants.
How does the value of each constant affect the graph of the standard sine function? Be specific.
A is
Chapter 1 - Worksheet 6 - TRIGONOMETRY PART 2
NAME_
1. Sketch the angle in standard position. Then find the exact values for cos and tan .
A. =
7
3
B. =
5
4
C. =
5
6
D. =
7
is in the 4th quadrant with reference angle .
3
3
3
sin
1
3=
2 = 3
cos =
and tan
WS1-FUNCTIONS
NAME_
1. As you travel at a fairly constant speed from Tucson to Bisbee (94 miles), you pass through Benson.
Benson is 40 miles from Tucson. Sketch graphs to represent the functions below. Label your graphs.
Hint: See a similar example in Ex