Use the guidelines of this section to sketch the curve. y = 1/(1+ e x ) Data
Question:
Use the guidelines of this section to sketch the curve.
y = 1/(1+ e–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 = 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 xhas 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: 0% (1 review)
The graph of ...View the full answer
Answered By
Cristine kanyaa
I possess exceptional research and essay writing skills. I have successfully completed over 5000 projects and the responses are positively overwhelming . I have experience in handling Coursework, Session Long Papers, Manuscripts, Term papers, & Presentations among others. I have access to both physical and online library. this makes me a suitable candidate to tutor clients as I have adequate materials to carry out intensive research.
4.90+
1538+ Reviews
3254+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Graph each system of inequalities. y - x = 4 -5 y 5
-
Add or subtract as indicated. x x + 5 1 25 x + 5
-
Solve each equation. Check the solutions. 2 X + 2-x X = = 5
-
rn rn Anushka (an Australian Tax resident) works as an employee for a child care centre, Brilliant Kids Pty Ltd, on a permanent part-time basis while she runs her business as a day carer for her own...
-
Describe the difference between activity-on-node and activity-on-arrow project networks.
-
Jerrison Company operates a wholesale hardware business. The following balance sheet accounts and balances are available for Jerrison at December 31, 2019. Required: 1. Prepare a classified balance...
-
Design teams are confronted with "multiobjective" decision making. Is it possible for objectives to lead to conflicting designs? Give an example(s).
-
At the end of its first year, the trial balance of Bronowski Company shows Equipment $30,000 and zero balances in Accumulated DepreciationEquipment and Depreciation Expense. Depreciation for the year...
-
Imagine two countries (A and B) operate in the Gold Standard era. The gold content of the country B's currency (B$) is twice that of the country A's currency (A$). The transportation cost of the gold...
-
Use Newtons method to find all roots of the equation correct to six decimal places. tan x = 1 x 2
-
Use the guidelines of this section to sketch the curve. y = e x /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)...
-
Consider the process + p p + 0 ( 0 photoproduction) with the proton at rest. (a) Find the minimum energy of the photon E . The Universe is filled by background electromagnetic radiation at the...
-
How does the unequal control of environmental resources contribute to global power imbalances, and what international agreements or frameworks can address environmental justice and promote...
-
KFC Turnaround Strategy New management today is incredibly deliberate about making the KFC brand relevant again. Theres two big ways for doing that, in the context of this industry: and that is...
-
The following algorithm computes n!: int factorial(n int) { } if (n = 1) return 1; return factorial (n-1) n; What is a reasonable definition of the corresponding recurrence relation T(n)?
-
Prasad's company has initial investment 6 6 0 0 0 and cash flows for each year 1 1 0 0 0 for 7 years , what is the IRR of the company?
-
Discount Suit Manufacturers produce diving suits for use in deep-sea diving. Its Standard Cost Card developed in December 2021 was as follows: Uniform Quantity Unit cost Direct materials for each...
-
Expand the spreadsheet of problem 13 to consider one extra source of return and one extra cost to using margin. Specifically, modify the spreadsheet to include expected dividends per share and the...
-
For each of the following transactions, indicate whether it increases, decreases, or has no effect on the following financial ratios: current ratio, debt-to-equity ratio, profit margin ratio, and...
-
Trace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of Example 1 to sketch the graph of f' below it. yA
-
The deck of a bridge is suspended 275 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y 275 -...
-
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. x? 9 lim x3 X - 3 lim (x + 3)
-
A sequential circuit has 3 flip-flops, A, B, C;one input x; one output y. The state diagram is shown below. Thecircuit is to be designed by treating the unused states asdont care conditions. The...
-
Write the definition of a function isEven , whichreceives an integer parameter and returns true if the parameter'svalue is even, and false otherwise. So if the parameter's value is 7 or 93 or 11 the...
-
Assume that an array of int s named a has beendeclared with 12 elements. The integer variable k holds avalue between 0 and 6. Assign 15 to the array element whose indexis k .
Study smarter with the SolutionInn App