Use the guidelines of Section 4.5 to sketch the curve. y = xe 2x Data from section
Question:
Use the guidelines of Section 4.5 to sketch the curve.
y = xe–2x
Data from section 4.5
Transcribed Image Text:
GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x) by hand. Not every item is relevant to every function. (For instance, a given curve might not have an asymptote or possess symmetry.) But the guidelines provide all the information you need to make a sketch that displays the most important aspects of the function. A. Domain It's often useful to start by determining the domain D of f, that is, the set of values of x for which f(x) is defined. B. Intercepts The y-intercept is f(0) and this tells us where the curve intersects the y-axis. To find the x-intercepts, we set y = 0 and solve for x. (You can omit this step if the equation is difficult to solve.) C. Symmetry (1) If f(-x) = f(x) for all x in D, that is, the equation of the curve is unchanged when x is replaced by -x, then f is an even function and the curve is symmetric about the y-axis. This means that our work is cut in half. If we know what the curve looks like for x > 0, then we need only reflect about the y-axis to obtain the complete curve [see Figure 3(a)]. Here are some examples: y = x²y = x¹, y = |x|, and y = cos x. (ii) If f(-x) = -f(x) for all x in D, then f is an odd function and the curve is symmetric about the origin. Again we can obtain the complete curve if we know what it looks like for x > 0. [Rotate 180° about the origin; see Figure 3(b).] Some simple examples of odd functions are y = x, y = x³, y = x³, and y = sin.x. (iii) If f(x + p) = f(x) for all x in D, where p is a positive constant, then f is called a periodic function and the smallest such number p is called the period. For instance, y = sin x has period 27 and y = tan x has period . If we know what the graph looks like in an interval of length p, then we can use translation to sketch the entire graph (see Figure 4).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (2 reviews)
The graph of ...View the full answer
Answered By
Briana Proulx
During the past several years, I have worked alongside numerous educational organizations aimed at providing accessible science education to the public. In 2012, I partnered with the Northeastern Massachusetts Aquaculture Center and A Coast for Every Classroom in a program created to educate K-12 teachers on the ecology and natural history of Massachusetts, in order to incorporate these elements into future lesson plans. Through that program, and in collaboration with Cat Cove Marine Laboratory and Salem State University, I published a series of fact sheets that would act as an identification guide to common intertidal marine species to further the students’ understanding of the habitats located in their own backyards. This same year, I worked as an aquaculture laboratory technician at Cat Cove Marine Laboratory, where, in addition to my aquaculture maintenance duties, I led educational tours and provided introductory marine biology and ecology lessons to visiting middle and high school students. In 2015, I worked as a research assistant at Salem State University, where I collected, compiled, and analyzed climatology data, phenology data, and primary literature sources as a part of a team conducting ongoing research on the effect of climate change on Rosaceae species within Essex County. We presented our preliminary findings at a research symposium sponsored by Sigma Xi, a scientific research honors society, in 2015. That same year, and in partnership with Salem State University, Universidad San Fransisco de Quito, and the Galápagos Academic Institute for the Arts and Sciences, I wrote two literature syntheses, The Effect of Feral Goat Eradication, Endemic Cacti Population Decline, and Woody Vegetation Population Growth on Galápagos Tortoise Population Trends within the Galápagos Islands and Analysis of Annual Migratory Paths to Assess Conservation Actions to Preserve Monarch Populations within the United States and Mexico. Most recently, I have worked as an online tutor for Chegg Tutors in the subjects of agricultural science, animal sciences, basic science, biology, earth science, English, environmental science, literature, natural sciences, study skills, and writing. During my time at Chegg Tutors, I assisted students in drafting, revising, editing, reformatting, and fact-checking essays, technical reports, and other academic papers.
0.00
0 Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.
-
Use the guidelines of Section 4.5 to sketch the curve. y = sin 2 x 2 cos x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve...
-
Use the guidelines of Section 4.5 to sketch the curve. y = x2 + x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y = f(x)...
-
Exercises 11-16: For the measured quantity, state the set of numbers that most appropriately describes it. Choose from the natural numbers, integers, and rational numbers. Explain your answer....
-
What factors are commonly used to evaluate suppliers?
-
You are an accounting intern working for Spring Fit Corporation. You have recently been assigned to help one of the accountants who is doing an internal audit of the business. You will be assisting...
-
Air expands adiabatically through a turbine from a pressure and temperature of \(180 \mathrm{psia}, 1600{ }^{\circ} \mathrm{R}\) to a pressure of \(14.7 \mathrm{psia}\). If the actual temperature...
-
Assume that you recently graduated with a major in finance and just landed a job in the trust department of a large regional bank. Your first assignment is to invest $100,000 from an estate for which...
-
Write a MIPS assembly code with minimum possible assembly instructions for the following C++.. Assume that the variables num1, num2 and num3 are already saved in some MIPS registers. if (x > 0 && y...
-
Find f. f'"(t) = t t
-
Use Newtons method to find all the roots of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations. e arctan x = x 3 + 1
-
A medical researcher wishes to test the effects of two different diets and two different exercise programs on the glucose level in a persons blood. The glucose level is measured in milligrams per...
-
On October 1, 20Y8, Jacinto Suarez and Tricia Fritz form a partnership. Suarez agrees to invest $20,890 in cash and inventory valued at $56,320. Fritz invests certain business assets at valuations...
-
Coma Corporation v. Kansas Department of Labor Who is the plaintiff? The defendant? The appellant? The appellee? What is the history of the case? Possible questions to answer would be: Who won at...
-
A block of mass 0.2 kg is pushed to be accelerated from rest to a speed of 4 m/s on a smooth surface. It then starts to climb up on a smooth slope. How high does the block climb on the slope until it...
-
Discuss the intricacies of memory management in contemporary operating systems, highlighting techniques like virtual memory, demand paging, and memory segmentation .
-
One of the radioactive isotopes used in medical treatment or analysis is phosphorus-32. The half-life of phosphorus-32 is 14 days. How many days is/are required for the activity of a sample of...
-
A manufacturer must decide whether to extend credit to a retailer who would like to open an account with the firm. Past experience with new accounts indicates that 45% are high-risk customers, 35%...
-
(a) Use integration by parts to show that (b) If f and g are inverse functions and f' is continuous, prove that (c) In the case where f and t are positive functions and b > a > 0, draw a diagram to...
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If a n is divergent, then |a n | is...
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If f (x) = 2x - x 2 + 1/3 x 3 - converges...
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If {a n } and {b n } are divergent, then {a...
-
Lucido Products markets two computer games: Claimjumper and Makeover. A contribution format income statement for a recent month for the two games appears below: Claimjumper Makeover $ 57,000 7,550...
-
Oriole Consumer Products Company Income Statement Net sales $61,560 Cost of products sold 22,400 Gross profit $39,160 Marketing, research, administrative expense 16,700 Depreciation 930 Operating...
-
Hanging Vine Inc. has decided to use the high-low method to estimate costs. The data for various levels of production are as follows: table cellspacing="0" cellpadding="3" class="narrative2"...
Study smarter with the SolutionInn App