This document provides 28 tutorials that construct function tables and graphs for rational functions of the form f(x) = a/(bx + c) + d, where a, b, c, and d are varied constants. Each tutorial works through an example of representing a rational function in both tabular and graphical form.
MODULE 5 QuizQuestion1. Find the domain of the function. E.docxmoirarandell
MODULE 5 Quiz
Question
1.
Find the domain of the function. Express your answer in interval notation.
a.
b.
c.
d.
2.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
3.
Graph f(x) = |x – 1|.
a.
b.
c.
d.
4.
Determine whether the function is even, odd, or neither. f(x) = x5 + 4
a. Even
b. Odd
c. Neither
5.
Find the value of f(3) if f(x) = 4x2 + x.
a. 38
b. 39
c. 40
d. 41
6.
Use the graph of the function to estimate: (a) f(–6), (b) f(1), (c) All x such that f(x) = 3
a. (a) 4 (b) 3 (c) –5, 1
b. (a) 5 (b) 4 (c) –3, 1
c. (a) 1 (b) 2 (c) –5, 2
d. (a) 7 (b) 5 (c) –5, 6
7.
The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.
a.
b.
c.
d.
8.
Evaluate f(–1).
a. –1
b. 8
c. 0
d. –2
9.
Determine whether the function is even, odd, or neither. f(x) = x3 – 10x
a. Even
b. Odd
c. Neither
10.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
11.
Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y. x|y| = x + 5
a. A function with domain all real numbers
b. A function with domain all real numbers except 0
c. Not a function: when x = 0, y = ±5
d. Not a function: when x = 1, y = ±6
12.
Graph y = (x – 2)2 + 1
a.
b.
c.
d.
13.
Find the y-intercept(s).
a. –2
b. 1, –3
c. –3
d. None
14.
Determine whether the correspondence defines a function. Let F be the set of all faculty teaching Chemistry 101 at a university, and let S be the set of all students taking that course. Students from set S correspond to their Chemistry 101 instructors.
a. A function
b. Not a function
15.
Determine whether the function is even, odd, or neither. f(x) = –4x2 + 5x + 3
a. Even
b. Odd
c. Neither
16.
Indicate whether the table defines a function.
a. Function
b. Not a function
17.
Use the graph of the function to estimate: (a) f(1), (b) f(–5),and (c) All x such that f(x) = 3
a. (a) –3 (b) –9 (c) 7
b. (a) –3 (b) –9 (c) –1
c. (a) 5 (b) –1 (c) 7
d. (a) 5 (b) –1 (c) –1
18.
Find the intervals over which f is increasing.
a. (–∞, –2], [1, ∞)
b. (–3, ∞)
c. (–∞, –3], [1, ∞)
d. None
19.
Evaluate f(4).
a. 4
b. 10
c. 5
d. –2
20.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
21.
Sketch the graph of the function f(x) = –2x + 3.
a.
b.
22.
Find the intervals over which f is decreasing.
a. (–∞, –2), [1, ∞)
b. (–∞, –2], [1, ∞)
c. (–∞, –3), [1, ∞)
d. (–∞, –3], [1, ∞)
23.
Indicate whether the table defines a function.
a. Function
b. Not a function
24.
Indicate whether the graph is the graph of a function.
a. ...
M166Calculus” ProjectDue Wednesday, December 9, 2015PROJ.docxinfantsuk
M166
“Calculus” Project
Due: Wednesday, December 9, 2015
PROJECT WORTH 50 POINTS –
1) NO LATE SUBMISSIONS WILL BE ACCEPTED
2) COMPLETED PROJECTS NEED TO BE LEGIBLE
I. Computing Derivatives (slope of curve at a point) of polynomial functions.
For each of the following functions in a.-e. below perform the following three steps:
1. compute the difference quotient
2. simplify expression from part 1. such that h has been canceled from the denominator
3. substitute and simplify
a.
b.
c.
d.
e. consider , using the results from parts a. through d.,
f. find a general formula for (steps 1 through 3 performed).
II. Show that
Consider the unit circle with in standard position in QI.
a. show that the area of the right triangle (see diagram) is
b. show that the area of the sector (see diagram) is
c. show that the area of the acute triangle (see diagram)
d. set up the inequality
e. multiply the inequality in part d. by . (direction of inequalities is unchanged)
f. take the reciprocal of each term from part e. The direction of the inequality must be reversed because .
g. plug in 0 for for only. The result should be
III. Show that
a. multiply by
b. use trigonometric identity to rewrite the numerator of the expression in part a. in terms of
c. factor the expression in part b. with one factor equal to . (find remaining factor).
d. use the fact that and substitute in the second factor (result is 0)
IV. Show that derivative of
a. find the difference quotient for
(use sum angle formula )
b. factor out of the two terms in the numerator with in part a
c. split up the expression in part b with each term over the denominator h
d. use identities to simplify part c. to
Thus you have shown that if .
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MATH133: Unit 3 Individual Project 2B Student Answer Form
Name (Required): ____Michael Magro_________________________
Please show all work details with answers, insert the graph, and provide answers to all the critical thinking questions on this form for the Unit 3 IP assignment.
A version of Amdah ...
Math 107 Final ExaminationSummer, 20151Math 107 College Algebr.docxandreecapon
Math 107 Final ExaminationSummer, 20151
Math 107 College AlgebraName______________________________
Final Examination: Summer, 2015Instructor __Professor Feinstein________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
There are 30 problems.
Problems #1-12 are multiple choice. Record your choice for each problem.
Problems #13-21 are short answer. Record your answer for each problem.
Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
(
Please sign (or type) your name below the following honor statement:
I have completed this
final examination
myself,
working independently and not consulting anyone except the instructor.
I have neither given nor received help on this final examination.
Name ____________
______
___
Date___________________
)
MULTIPLE CHOICE. Record your answer choices.
1.7.
2.8.
3.9.
4.10.
5.11.
6.12.
SHORT ANSWER. Record your answers below.
13.
14.
15.
16.
17.
18.
19. (a)
(b)
(c)
20. (a)
(b)
(c)
(d)
21. (a)
(b)
(c)
(d)
SHORT ANSWER with Work Shown. Record your answers and work.
Problem Number
Solution
22
Answers:
(a)
(b)
Work/for part (a) and explanation for part (b):
23
Answers:
(a)
(b)
(c)
Work for part (a):
24
Answer:
Work:
25
Answer:
Work:
26
Answers:
(a)
(b)
Work for part (a) and for part (b):
27
Answer:
Work:
28
Answer:
Work:
29
Answers:
(a)
(b)
Work for (b):
30
Answer:
Work:
College Algebra MATH 107 Summer, 2015, V1.4
Page 1 of 11
MATH 107 FINAL EXAMINATION
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator. You must complete the exam individually.
Neither collaboration nor consultation with others is allowed.
Record your answers and work on the separate answer sheet provided.
There are 30 problems.
Problems #1–12 are Multiple Choice.
Problems #13–21 are Short Answer. (Work not required to be shown)
Problems #22–30 are Short Answer with work required t ...
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In this issue of Math in the News we explore logarithmic functions to model the thawing of frozen turkeys. We look at USDA guidelines to determine data points and use a graphing calculator to create mathematical models.
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2. Overview
This set of tutorials provides 28 examples of
rational functions in tabular and graph form.
3. Tutorial--Rational Functions in Tabular and Graph Form: Example 01. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) for a = 1, b = 1, c = 0.
4. Tutorial--Rational Functions in Tabular and Graph Form: Example 02. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) for a = -1, b = 1, c = 0.
5. Tutorial--Rational Functions in Tabular and Graph Form: Example 03. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) for a = 1, b = -1, c = 0.
6. Tutorial--Rational Functions in Tabular and Graph Form: Example 04. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) for a = -1, b = -1, c = 0.
7. Tutorial--Rational Functions in Tabular and Graph Form: Example 05. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) for a = 1, b = 1, c = 1.
8. Tutorial--Rational Functions in Tabular and Graph Form: Example 06. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) for a = -1, b = 1, c = 1.
9. Tutorial--Rational Functions in Tabular and Graph Form: Example 07. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) for a = 1, b = -1, c = 1.
10. Tutorial--Rational Functions in Tabular and Graph Form: Example 08. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) for a = 1, b = 1, c = -1.
11. Tutorial--Rational Functions in Tabular and Graph Form: Example 09. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) for a = -1, b = -1, c = 1.
12. Tutorial--Rational Functions in Tabular and Graph Form: Example 10. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) for a = -1, b = 1, c = -1.
13. Tutorial--Rational Functions in Tabular and Graph Form: Example 11. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) for a = 1, b = -1, c = -1.
14. Tutorial--Rational Functions in Tabular and Graph Form: Example 12. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) for a = -1, b = -1, c = -1.
15. Tutorial--Rational Functions in Tabular and Graph Form: Example 13. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = 1, b = 1, c = 1, d = 1.
16. Tutorial--Rational Functions in Tabular and Graph Form: Example 14. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = 1, b = 1, c = 1, d = -1.
17. Tutorial--Rational Functions in Tabular and Graph Form: Example 15. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = -1, b = 1, c = 1, d = 1.
18. Tutorial--Rational Functions in Tabular and Graph Form: Example 16. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = -1, b = 1, c = 1, d = -1.
19. Tutorial--Rational Functions in Tabular and Graph Form: Example 17. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = 1, b = -1, c = 1, d = 1.
20. Tutorial--Rational Functions in Tabular and Graph Form: Example 18. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = 1, b = -1, c = 1, d = -1.
21. Tutorial--Rational Functions in Tabular and Graph Form: Example 19. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = 1, b = 1, c = -1, d = 1.
22. Tutorial--Rational Functions in Tabular and Graph Form: Example 20. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = 1, b = 1, c = -1, d = -1.
23. Tutorial--Rational Functions in Tabular and Graph Form: Example 21. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = -1, b = -1, c = 1, d = 1.
24. Tutorial--Rational Functions in Tabular and Graph Form: Example 22. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = -1, b = -1, c = 1, d = -1.
25. Tutorial--Rational Functions in Tabular and Graph Form: Example 23. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = -1, b = 1, c = -1, d = 1.
26. Tutorial--Rational Functions in Tabular and Graph Form: Example 24. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = -1, b = 1, c = -1, d = -1.
27. Tutorial--Rational Functions in Tabular and Graph Form: Example 25. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = 1, b = -1, c = -1, d = 1.
28. Tutorial--Rational Functions in Tabular and Graph Form: Example 26. In this
tutorial, construct a function table and graph for a rational function of the
form f(x) = a/(bx + c) + d for a = 1, b = -1, c = -1, d = -1.
29. Tutorial--Rational Functions in Tabular and Graph Form: Example 27. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = -1, b = -1, c = -1, d = 1.
30. Tutorial--Rational Functions in Tabular and Graph Form: Example 28. In this
tutorial, construct a function table and graph for a rational function of the form
f(x) = a/(bx + c) + d for a = -1, b = -1, c = -1, d = -1.