Use the guidelines of this section to sketch the curve. y = x/x 2 + 1 Data
Question:
Use the guidelines of this section to sketch the curve.
y = x/√x2 + 1
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 = x, 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% (4 reviews)
The graph o...View the full answer
Answered By
Nyron Beeput
I am an active educator and professional tutor with substantial experience in Biology and General Science. The past two years I have been tutoring online intensively with high school and college students. I have been teaching for four years and this experience has helped me to hone skills such as patience, dedication and flexibility. I work at the pace of my students and ensure that they understand.
My method of using real life examples that my students can relate to has helped them grasp concepts more readily. I also help students learn how to apply their knowledge and they appreciate that very much.
4.00+
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...
-
Why might a cheap location not be the best location?
-
Three mountain climbers who are roped together in a line are ascending an ice field inclined at 31.0 to the horizontal (Fig. 4-69). The last climber slips, pulling the second climber off his feet....
-
Let x represent the number of registers in use at a departmental store. Determine whether the random variable x is discrete or continuous. Explain.
-
Hickey Corporation is a manufacturer that produces a single product. The following information has been taken from the companys production, sales, and cost records for the just completed year:...
-
If a sensor (I1:0) is used to count the incoming cars, and another sensor (I1:1) is used to count the outgoing cars, please design a PLC program such that when the number of cars in the parking lot...
-
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. x 6 x 5 6x 4 x 2 + x + 10 = 0
-
Use the guidelines of this section to sketch the curve. y = x 2 + x 2 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve y =...
-
At the end of 2008, Lucretia McEvil Company has $180,000 of cumulative temporary differences that will result in reporting future taxable amounts as follows. 2009 .....$ 60,000 2010 .....50,000 2011...
-
1. The kinetic energy of a skier at a small hill (Point A) and his potential energy are 120 kJ and 450 kJ, respectively. Then the skier slides down the smooth snow-covered hill to the flat leveled...
-
A block attached to a spring of the spring constant k = 500 N/m is pulled to stretch the spring by 0.40 m from the equilibrium point. Next moment, the block is released. When the block passes the...
-
What is the relative benefits index? (make sure to make a note of this on a separate piece of paper, you will need it later).
-
A 83-gram sample of water that has an initial temperature of 8.0 C absorbs 6722 joules. If the specific heat of water is 4.184 J/(g C), what is the final temperature of the water? You must show all...
-
7. The following question uses RSA Algorithm. Assume p = 13 and q = 17. Encryption key e has to be at least 10 such that e is relatively prime to (p-1)*(q-1). Complete calculation must be shown for...
-
Ford is going to produce a new vehicle, the Pioneer, and wants to determine the amount of annual capacity it should build. Fords goal is to maximize the profit from this vehicle over the next 10...
-
The unadjusted trial balance of Secretarial Services is as follows: SECRETARIAL SERVICES Unadjusted Trial Balance as at 31 December 2017 Account Debit Credit Cash at bank Office supplies Prepaid...
-
Describe in words the region of R 3 represented by the equation(s) or inequality. y < 8
-
Describe in words the region of R 3 represented by the equation(s) or inequality. y = -2
-
Describe in words the region of R 3 represented by the equation(s) or inequality. z > -1
-
What is Database software, presentation software, Multimedia software, Personal Digital Assistant (PDA)? Please Explain Elaborately with examples. What are different types of database such as SQL,...
-
Furnittio1 Furnittio is a small enterprise dedicated to the production of special fittings for doors. After decades in the business, Furnittio created a new type of opening for interior doors in...
-
2. Let $f(x, y, z)=x e^{x y z}-\arcsin \left(2 x+y^{2} ight)-z y+2$ be a function of three variables. (a) Find the domain of definition of the above function and decide if it is closed or open,...
Study smarter with the SolutionInn App