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Graphs and Functions

Onto or One-to-one

Let f(s) = string s with 01100 concatenated. Example: f(0000) = 000001100 Show: a) the range of f b) f is onto c) f is one-one

Graphs of Trigonometric Functions

Draw the graphs of the following trigonometric functions and mark the asymptotes and intercepts. (1) y = 2 sin(0.5x) (2) y = cot(pi x) (3) y = -cos(2x + pi)

Graph each section

Need the solution and the graph for each question. Also if possible please show the graph on the graphing paper.

Suppose f and g are functions analytic in a domain D.

Suppose f and g are functions analytic in a domain D. If z_n is a bounded sequence of distinct points in D and if f(z_n) = g(z_n) for all n, show that f(z) = g(z) for all z in D. Is the same true for an unbounded sequence?

Finding discriminant, roots and graphing quadratic functions

1) Solve 6x2 + 3x - 18 = 0 using the quadratic formula. Read the information in the assignment list to learn more about how to type math symbols, such as the square root. 2) Use the graph of y = x2 + 4x - 5 to answer the following: a) Without solving the equation, use the graph to determine the solution(s) to the equat

Equations of lines

1. Write the equation of the line which has y-intercept (0, 5) and is perpendicular to the line with equation y = -3x + 1 2. Write the equation of the line passing through (-3, -5) and (3, 0).

Prove that the functions are subsets.

14. Let f: A --> B, D is a subset of A, and E is a subset of B. Prove that a) f(f^-1(E)) is a subset of E b) A - f^-1(E) is a subset of f^-1(B - E) c) f^-1(B - E) is a subset of A - f^-1(E). d) E = f(f^-1(E)) iff E is a subset of Rng(f) from Images of Sets. Prove for each part except (a) and (d) and explain each step

Derivatives and graphing

Derivatives and graphing; please show all work. See attached. Pg 176 #24 For the function, f, given in the graph in following figure: a) sketch f ' (x) b) Where does f ' (x) change its sign? c) Where does f ' (x) have local maxima or minima? #25 Using the answer to previous problem as a guide, write a

Equation of Hyperbola and also ellipse.

#1. find the center,foci and vertices of ellipse. (x+4)^2/49 + (Y+4)^2/25 =1 #2. Find the center, transverse,axis,vertices,foci and asymptotes. Graph the equation y^2-x^2=100 #3. find the equation of hyperbola. Vertices (-1,5) and (9,-5) Asymptote the line y+5=6/5 (x-4) write the equatio

Problems on Parabola, Ellipse and Hyperbola

#1. Find the equation of parabola describe. Find 2 points of latus rectum.Graph. Focus(-5,0) Vertex(0,0) #2 Find the equation of the parabola. Find 2 points that define latus rectum. Graph. Focus (0,1) Diectrix line y= -1 #3. Find the equation of ellipse.draw the graph. Center (0,0) Focus(0,8) Vertex (

Minimum, maximum, critical point

Please show work where applicable. Some graphing needed. #5 The function f(x)=x^4 - 4x^3 + 8x has a critical point at x=1. Use the second derivative test to identify it as a local maximum, a local minimum or neither. Using calc or computer, graph the following functions. Describe briefly in words the interesting features o


Which of the following are functions? 1. f(x) = 2 if x > 1 otherwise f(x) = -1 2. f(x) = 5 if x > 0 or f(x) = -5 if x < 0 or f(x) = 5 or -5 if x = 0 3. f(x) = x/10

Function as Power Series

Find a power series representation for the function and determine the interval of convergence. f(x)= 3/(1-x^4) Please show steps.

1. Economic production lot size problem. 2. Waiting line problem M/M/1 model

1. Kellam Images prints snack food bags on long rolls of plastic film. The plant operates 250 days a year. The daily production rate is 6000 bags, and the daily demand is 3500 bags. The cost to set up the design for printing is $300. The holding cost is estimated at 2 cents per bag. a. What is the recommended production lot s

Math Proof

College level proof before real analysis. Please explain each step of your solution. Thank you.

Given the function, find the value, f (-2)

Please answer the following questions to these two math questions. I need to know how to answer them and how you got the answers. Please give me a full explanation of them and show your complete work. Thanks

Functions : Odd, Even, One-to-one, Domain, Range and Function Composition

Practice Problems Compare the graph of the given quadratic function f with the graph of y = x2. 1) f(x) = (x - 2)2 + 3 Determine if the function is even, odd, or neither. 2) f(x) = 2x5 + 2x3 Decide whether the relation defines a function. 3) {(-8, 2), (-8, 8), (-1, 8), (5, 6), (8, 7)} 5) y2 = 3x Find the domain

Graphical solution - Objective function coefficient

Use a graph to illustrate why a change in an objective function coefficient does not necessarily lead to a change in the optimal values of the decision variables, but a change in the right-hand sides of a binding constraint does lead to new values.

Parametric equations

Please see the attached file. If a = 5 and b = 4, find parametric equations for the curve that consists of all possible positions of the point P in the figure, using the angle &#952; as the parameter. The line segment AB is tangent to the larger circle.