Use the guidelines of this section to sketch the curve. y = x 2 + x
Question:
Use the guidelines of this section to sketch the curve.
y = √x2 + x – 2
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 o...View the full answer
Answered By
Shubhradeep Maity
I am an experienced and talented freelance writer passionate about creating high-quality content. I have over five years of experience working in the field and have collaborated with several renowned companies and clients in the SaaS industry.
At Herman LLC, an online collective of writers, I generated 1,000+ views on my content and created journal content for 100+ clients on finance topics. My efforts led to a 60% increase in customer engagement for finance clients through revamping website pages and email interaction.
Previously, at Gerhold, a data management platform using blockchain, I wrote and published over 50 articles on topics such as Business Finance, Scalability, and Financial Security. I managed four writing projects concurrently and increased the average salary per page from $4 to $7 in three months.
In my previous role at Bernier, I created content for 40+ clients within the finance industry, increasing sales by up to 40%.
I am an accomplished writer with a track record of delivering high-quality content on time and within budget. I am dedicated to helping my clients achieve their goals and providing exceptional results.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Solve each equation. Check the solutions. 14 x -= x - 5
-
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.
-
Use the guidelines of this section to sketch the curve. y= sin x/1 + cos x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y...
-
The inequality describes the range of monthly average temperatures T in degrees Fahrenheit at a certain location. (a) Solve the inequality. (b) If the high and low monthly average temperatures...
-
What types of information can an entrepreneur collect from census data?
-
How is a scorecard different from a dashboard?
-
7. Jason Jacque was riding as a passenger in a car driven by his sister, who was drunk and driving 19 mph over the speed limit. She failed to negotiate a curve, skidded off the road, and collided...
-
1. Draw an ERD for the Parrot Palace information system. 2. Indicate cardinality. 3. Identify all fields you plan to include in the birds and tricks tables. For example, in the bird table, you might...
-
NPV unequal lives Grady Enterprises is looking at two project opportunities for a parcel of land the company currently owns. The first projeds a restaurant, and the second project is a sports...
-
Use the guidelines of this section to sketch the curve. y = x/x 2 + 1 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 = 2x 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)...
-
Explain the purpose of a proof of cash. List two types of misstatements it is meant to uncover.
-
The figure below is meant to model a rectangular coil composed of 100 tightly packed turns of wire. The rectangular loops are all identical with dimensions 30.0 cm x 40.0 cm and a current of 1.20 A...
-
Coronado Company lends Wildhorse Company $9600 on April 1, accepting a four-month, 8% interest note. Coronado Company prepares financial statements on April 30. What adjusting entry should be made...
-
These videos introduce ideas that may or may not coincide with the week's learning objective or theme. Why do you think this video was chosen to be included in this course? Watch the following video:...
-
Consider an investor who is holding one share of a stock whose price is evolving according to a standard Brownian motion process, i.e. = S(u) S(0)+oW(u), u0, where > 0 is the volatility coefficient....
-
Look at the picture below and Then briefly comment in the discussion: 1. What do you think is the point of the picture? 2. Is there anything else in your life that you can save money on like this?...
-
Dorno Corporation incurred expenses during the current year as follows: $2,300 delivery expense, $5,500 advertising expense, $13,750 sales salaries expense, $1,250 sales supplies expense, $12,750...
-
Distinguish between the work performed by public accountants and the work performed by accountants in commerce and industry and in not-for-profit organisations.
-
Describe in words the region of R 3 represented by the equation(s) or inequality. 0 < z < 6
-
Describe in words the region of R 3 represented by the equation(s) or inequality. y 2 = 4
-
Describe in words the region of R 3 represented by the equation(s) or inequality. z = -1 x? + y? = 4,
-
QLD The purpose of a Production Department, Budget include cot Lot project production cost figure by month (b) project revenue figures by month 2) project unit sales figure by month. (d) fall of the...
-
VSOE" stands for: "Vendor-specific objective evidence." O "Vendor substantiation of earnings." O "Variable set overhead earned." O "Value-specified operating earnings
-
Please answer with reason for all why the option is correct and why the other options are incorrect,, Please help with this Accounting type Question: The current ratio is ratio between: A . Current...
Managerial Accounting Method And Meaning Chapman And Hall 1st Edition - ISBN: 0278000215 - Free Book
Study smarter with the SolutionInn App