Use the guidelines of this section to sketch the curve. y = 2x x Data from
Question:
Use the guidelines of this section to sketch the curve.
y = 2√x – 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: 66% (3 reviews)
The grap...View the full answer
Answered By
Fahmin Arakkal
Tutoring and Contributing expert question and answers to teachers and students.
Primarily oversees the Heat and Mass Transfer contents presented on websites and blogs.
Responsible for Creating, Editing, Updating all contents related Chemical Engineering in
latex language
4.40+
8+ Reviews
22+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Find all real solutions. Check your results. 1. X 2 X 5
-
Solve each equation. Check the solutions. 14 x -= x - 5
-
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...
-
At one time the Thames River in England supported an abundant community of fish. Pollution then destroyed all the fish in a 40-mile stretch near its mouth for a 45-year period beginning in 1915....
-
Why is it important to discover more than just the number of passersby in a traffic count?
-
Two blocks made of different materials, connected by a thin cord, slide down a plane ramp inclined at an angle to the horizontal, Fig. 4-76 (block B is above block A). The masses of the blocks are mA...
-
The mean number of droughts in Asia per year from 1980 through 2008 was about 3.24. Find the probability that the number of droughts in Asia in any given year from 1980 through 2008 are (a) exactly...
-
Titan Mining Corporation has 8.5 million shares of common stock outstanding, 250,000 shares of 5 percent preferred stock outstanding, and 135,000 7.5 percent semiannual bonds outstanding, par value...
-
Construct the mathematical function that describes the movement of the piston. 1.Relevant calculations and construction of the algebraic model. Parameter adjustment If the distance d that the piston...
-
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 =...
-
Use Newtons method to approximate the indicated root of the equation correct to six decimal places. The root of 2.2x 5 4.4x 3 + 1.3x 2 0.9x 4.0 = 0 in the interval [2, 1]
-
A player tosses two coins and receives $5 if 2 heads turn up, loses $4 if 1 head turns up, and wins $2 if 0 heads turn up. Compute the expected value of the game. Is the game fair?
-
A constant force F = 9.00 +9.00 N acts on a 2.00 kg mass. Determine the work done when the mass moves through the displacements r given below. (a) r = 3.00 m (b) r = 4.00 m (c) r = 3.00 + 4.00 m
-
Driving down the road at a speed of 30.1 m/s, you suddenly notice a fallen tree blocking the road a distance of 55.1 m ahead of you. You step on the brake pedal and decelerate at a constant rate....
-
A cylinder contains a gas at temperature 200C (715 celcius), volume 5 litres (4I) and a pressure of 2.2MPa (130kPa). The polytropic process index value (n) of the gas in its initial state is 1.1....
-
On planet #2, you launch a projectile straight up from the ground at a speed of 43.3 m/s. The projectile reaches a maximum height of 63.3 m before falling back to the ground. What is the value of g...
-
How do modern operating systems implement security features such as access control, authentication, and encryption to protect system resources and data integrity, considering both discretionary and...
-
FineHair is developing a new product to promote hair growth in cases of male pattern baldness. If FineHair markets the new product and it is successful, the company will earn $1,000,000 in additional...
-
Economic feasibility is an important guideline in designing cost accounting systems. Do you agree? Explain.
-
Describe in words the region of R 3 represented by the equation(s) or inequality. x + y? = 4|
-
Describe in words the region of R 3 represented by the equation(s) or inequality. x + y? + z? = 4
-
Describe in words the region of R 3 represented by the equation(s) or inequality. x? + y? + z? < 4 4
-
Your answer should be as complete as possible. Do not deal just with conclusions. Example: if you say that a contract exists, that is a conclusion. Explain why you believe that a contract was or was...
-
Specific Security Agreement - Agreement that secures certain specific assets as collateral (ie. debtor purchases a vehicle) Registered at the Personal Property Registry (PPR). Creditor has right to...
-
Dory is not feeling well. She is not sure if she has a flu or something worse. She goes to the fish clinic and sees Dr. Doolittle. Dr. Doolittle give her a shot of Bactracin and tells her she should...
Study smarter with the SolutionInn App