Use the guidelines of Section 4.5 to sketch the curve. y = 1/1 x 2 Data
Question:
Use the guidelines of Section 4.5 to sketch the curve.
y = 1/1 – x2
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 = x5, 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 xhas period 27 and y = tan x has period z. 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: 100% (3 reviews)
The graph of ...View the full answer
Answered By
Utsab mitra
I have the expertise to deliver these subjects to college and higher-level students. The services would involve only solving assignments, homework help, and others.
I have experience in delivering these subjects for the last 6 years on a freelancing basis in different companies around the globe. I am CMA certified and CGMA UK. I have professional experience of 18 years in the industry involved in the manufacturing company and IT implementation experience of over 12 years.
I have delivered this help to students effortlessly, which is essential to give the students a good grade in their studies.
3.50+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Use the guidelines of Section 4.5 to sketch the curve. y = x 4 3x 3 + 3x2 x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a...
-
Use the guidelines of Section 4.5 to sketch the curve. y = x 3 6x 2 15x + 4 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a...
-
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.
-
Murray Company has provided the following partial comparative balance sheets and the income statement for 2010. Required: Compute operating cash flows by using the indirectmethod. Murray Company...
-
Describe the process of manually crashing a project network.
-
Dave Krug contributed $1,000 cash along with inventory and land to a new partnership. The inventory had a book value of $800 and a market value of $2,000. The land had a book value of $1,400 and a...
-
Sometimes financial statements will show "unearned revenue." How does this arise? What type of transactions might be typical examples?
-
The following is taken from the Pinkston Company balance sheet. Interest is payable semiannually on January 1 and July 1.The bonds are callable on any semiannual interest date. Pinkston uses...
-
Everywhere Deliver Service paid $129,000 for a group purchase of land, building, and equipment. At the time of the acquisition, the land had a market value of $75,000, the building $43,000 and the...
-
Use the guidelines of this section to sketch the curve. y = e 2x e x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =...
-
Use the guidelines of this section to sketch the curve. y = x 2 + x x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =...
-
Philip Cutting Machinery takes custom orders for metal parts. In order to machine some of the parts, the shop uses various solvents that must be disposed of in compliance with local hazardous-waste...
-
What decision is made by a Medicare Administrative Contractor (MAC) regarding whether to cover a particular service on a MAC-wide basis?
-
Think about your experience serving on a team (Softball team)- preferably related to your current role(I plan to coach young adults) but other experiences on a team will work as well. Consider the...
-
Which course of action will you recommend? You suggest Angel choose the discounted special offer from the one cloud provider. You suggest Angel choose the best-of-breed services from multiple cloud...
-
Annotated Bibliography in Order An annotated bibliography is typically organized alphabetically, but for this project, we're going to combine it with a paper outline. This exercise will assist you in...
-
please as a reference take any Indian movie or tv show if possible Topics: This course is examining concepts of male and female in the west, and so your research topic should be something about...
-
Reingold & Feinstein found that its overhead and expenses were too high. It decided to hire an experienced law firm administrator to keep costs down and bring the profits of the firm up. As...
-
The following information is available for Partin Company: Sales $598,000 Sales Returns and Allowances 20,000 Cost of Goods Sold 398,000 Selling Expense 69,000 Administrative Expense 25,000 Interest...
-
If f and t are both even functions, is the product ft even? If f and t are both odd functions, is ft odd? What if f is even and t is odd? Justify your answers.
-
If f and t are both even functions, is f + t even? If f and t are both odd functions, is f + t odd? What if f is even and t is odd? Justify your answers.
-
Determine whether f is even, odd, or neither. You may wish to use a graphing calculator or computer to check your answer visually. f() = 1 + 3 3 -x 5
-
If two equal charges of 35.00 C each are separated in the air by a certain distance of 1.08x10 3 m, what is the magnitude of the force acting between them?
-
Assume you are a US exporter with an account receivable denominated in New Zealand dollars due in six months. You are considering different approaches to hedge currency risk. Based on the table below...
-
Suppose a Franco-Dutch Airline Company in Paris receives the following indirect quotes in New York: 0.92 - 3 and 0.63 - 4. Required: i. Based on the above information, determine the quotes for the...
Study smarter with the SolutionInn App