Use the guidelines of Section 4.5 to sketch the curve. y = x2 + x Data from
Question:
Use the guidelines of Section 4.5 to sketch the curve.
y = x√2 + x
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: 88% (9 reviews)
The graph of ...View the full answer
Answered By
Tamil Elakkiya Rajendran
I'm currently involved in the research in the field of Biothermodynamics, Metabolic pathway analysis and computational Biology. I always prefer to share my knowledge whatever I have learnt through my degree whenever time permits.
5.00+
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 = xe 2x 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) by...
-
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 = 3 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 =...
-
In Exercises 3542, describe and sketch the surface given by the function. f(x, y) = Jxy, 0, x 0, y 0 x <0 or y < 0
-
What is the economic order quantity? How does it minimize total inventory costs?
-
Suppose the kick in Example 3-6 is attempted 36.0m from the goalposts, whose crossbar is 3.05 m above the ground. If the football is directed perfectly between the goalposts, will it pass over the...
-
Air flows steadily between two sections in a duct. At section (1), the temperature and pressure are \(T_{1}=80^{\circ} \mathrm{C}, p_{1}=301 \mathrm{kPa}(\mathrm{abs})\), and at section (2), the...
-
1. If you were advising Squires management team on their impending decision, what would you tell them? 2. Is there an alternative to reduce the impacts of high diesel prices other than to develop...
-
The Hilbert matrix H is square matrix where row i and column j (using Python's zero indexing) of the n x n matrix are given by: 1 Aij for i = = 0,...,n 1, and for j = 0,...,n-1 i+j+1 For n=5 the...
-
Use the guidelines of this section to sketch the curve. y = 3 sin x sin 3 x Data from section 4.5 GUIDELINES FOR SKETCHING A CURVE The following checklist is intended as a guide to sketching a curve...
-
Find f. f"(x) = 6x + sin x
-
Suppose a filter has a transfer function given by H (f) = sinc2 (f). Find the noise equivalent bandwidth of the filter.
-
Evaluate the following postfix expression: 112 4/37*-5+
-
1. What is a special law? 2. LAW 54 -DO YOU THINK THE LAW FOR THE PREVENTION OF DOMESTIC VIOLENCE IS A DETERRENt OR PREVENT DOMESTIC ABUSE?WHY? 3. STALKING . Look up the Puerto Rico stalking law...
-
V 3. Find poles and zeros. Draw ROC. Find inverse z transform of the following signal X(z) = (z +0.1) (z-1.5z+0.5)
-
A tennis ball with a mass of 150 g is initially travelling at 15 m/s [E] when it is struck by a racket. The ball now is moving at 20 m/s [W]. If the time of contact between the racket and ball is...
-
A truck for hauling coal has an estimated net cost of $80000 and is expected to give service for 230000 kilometres. Its salvage value will be $4000 and depreciation will be charged at a rate of 33...
-
The purchasing agent for a PC manufacturer is currently negotiating a purchase agreement for a particular electronic component with a given supplier. This component is produced in lots of 1000, and...
-
Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. 10 5 + 2 cos 0
-
Find the sum of the series. 1 ( + 3) -1 (n
-
Find the sum of the series.
-
Express the repeating decimal 4.17326326326 . . . as a fraction.
-
Use the Laplace transform to solve the given initial value problem. $$ \begin{array}{1} y^{\prime \prime}-6 y^{\prime}+58 y=\delta _{1}(t) \\\ y(0)=-1, \quad y^{\prime}(0)=25 \end{array} $$...
-
When 10.1 g CaO is dropped into a styrofoam coffee cup containing 157 g H2O at 18.0C, the temperature rises to 35.8C. Calculate the enthalpy change of the following reaction in kJ/mol CaO. Assume...
-
Broken Hill Proprietary Company Limited (BHP) is an Australian multinational mining, metals and petroleum dual-listed public company which is currently the largest mining company in the world. Based...
Study smarter with the SolutionInn App