Use the guidelines of this section to sketch the curve. In guideline D find an equation of
Question:
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote.
y = 2x3 + x2 + 1/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 = 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: 100% (1 review)
The graph of the equatio...View the full answer
Answered By
Aqib Parvej
I am teaching since my graduation time so I have teaching experience of about 5 years and in these years I learn to teach in the best and interesting way .
4.80+
20+ Reviews
41+ 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 this section to sketch the curve. In guideline D find an equation of the slant asymptote. y = (x + 1) 3 /(x 1) 2 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The...
-
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote. xy = x 2 + 4 Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following...
-
In Exercises 118, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. (2.6, 1.3) and (1.6, -5.7)
-
Summarize the major exemptions and simplified registrations available to small companies wanting to make public offerings of their stock
-
Billiard ball A of mass mA = 0.120kg moving with speed vA = 2.80m/s strikes ball B, initially at rest, of mass mB = 0.140 kg. As a result of the collision, ball A is deflected off at an angle of 30.0...
-
Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters (in standardized units), describing the average characteristics of a wine in each cluster, are listed in the...
-
The Stearns Company uses a voucher system and records invoices at gross. Record the following transactions in the voucher register and/or check register as appropriate: 201X Dec. 1 Voucher no. 400...
-
Currently there is discussion by the members of NAFTA to form an optimum currency area. Support or do not support the creation of an optimum currency area. What are the advantages and disadvantages...
-
Find f. f'(x) = cos x (1 x 2 ) 1/2
-
Use the guidelines of this section to sketch the curve. In guideline D find an equation of the slant asymptote. y = e x x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following...
-
Using the following trial balance and adjustment data for Vivian?s Repair Co. of Windsor, prepare1.?A worksheet for October2. An income statement for October, a statement of owner?s equity for...
-
Use the following raw data to create a Financial Key Performance Indicator (KPI) on Microsoft Excel (please list steps) Then put together 1 slide of what would be the most important thing to present...
-
1 A clothing store buys sweaters for $48.00 less 47% for buying over 50 pairs, and less a further 11-% for buying last season's style. The sweaters are then marked up to cover overhead expenses of 1...
-
A current-carrying coil is used at Earth to measure the strength of the horizontal component of the Earth's magnetic field and to measure the deflection of a compass placed inside the coil. What...
-
1). A person stands directly in front of two speakers that are emitting the same pure tone. The person then moves to one side until no sound is heard. At that point, the person is 7.15 m from one of...
-
Marian Manufacturing (2M) applies manufacturing overhead to jobs based on direct labor costs. For Year 2, 2M estimates its manufacturing overhead to be $421,200 and its direct labor costs to be...
-
We related EVPI to the value of an envelope that contains the true ultimate outcome. This concept can be extended to less than perfect information. For example, in the Acme problem suppose that the...
-
If the jobs displayed in Table 18.24 are processed using the earliestdue-date rule, what would be the lateness of job C? TABLE 18.24 Processing Times and Due Dates for Five Jobs Job C D E...
-
Find a b. lal = 80, IbI =50, the angle between a and b is 3/4
-
If u is a unit vector, find u v and u w.
-
If u is a unit vector, find u v and u w. u V
-
Three particles are fixed on an x axis. Particle 1 of charge q is at x=-a and particle 2 of charge q2 is at x = +a. If their net electrostatic force on particle 3 of charge Q is to be zero, what must...
-
Let vectors A = (2, 1, -4), B = (-3, 0, 1), and C = (-1,-1,2). Calculate the following: V and V2 4 Part F are different vectors with lengths V and V2 respectively. Find the following: Express your...
-
A0.15-kg apple falls off a tree branch that is 2.7 m above the thick grass. The apple sinks 0.062 m into the grass while stopping. Part A Determine the average contact force that the grass alone...
Study smarter with the SolutionInn App