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Graphs and Functions

Justifying An Increased Line of Credit

Case 3: Justifying An Increased Line of Credit 1. A monthly regression analysis is to be conducted using monthly data for each demand variable. Formulate your empirical model using the additive functional form. 2. Using economic theory what are the hypothesized signs of parameters in the demand model. 3. Interpret your

Equivalence relations, surjective maps, partitions and fibers.

Consider any surjective map f from a set X onto another set Y. We can define a relation on X by x_1 ~ x_2 if f(x_1) = f(x_2). Check that this is an equivalence relation. Show that the associated partition of X is the partition into "fibers" f^(-1) (y) for y in Y. I would like to understand what this question is asking me a

Monte Carlo Methods : Cumulative Density Function

Show that if the value of a variable x is selected by inverting the cdf (cumulative density function), x = F^-1 (RN), the distribution of the x values is given by the function f(x). See attached file for full problem description.

Graph Theory, Necessary and sufficient condition digraphs to be Eulerian.

Page 90, Theorem 4.6 ( To show that a digraph is hamiltonian if and only if for each vertex v, indegree (v) =outdegree (v) Page 92 Exercise problem 4.1 ( A modified version of konigsberg problem where, two extra bridges are built. ) Page 93, Figure 4.5 need to show as Hamilton. (Show that dodecahedron is hami

Evaluating and Graphing Functions and Trigonometry Word Problems

(1) For the function: (see attached) a) Give the y values for x = -1, 0, 1, 2, 3, 4. b) Using these points, draw a curve. (2) For the equation , perform the following: (a) Solve for all values of x that satisfies the equation. (b) Graph the functions y = x and on the same graph (by plotting points if necessary). Sho

Graphing Linear Equations an Geometry of Coordinate Points

Please see the attached file for the fully formatted problems. Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept 1. Slope: -2; y-intercept: (0, 4) 2. Slope: 5; y-intercept: (0, -2) 3. Slope: ; y-intercept: (0, 8) 4. Find the slope of any line pe

Derivatives and Rate of Change Word Problems: Motion and Relative Speed

1.A body has an a equation of motion measured in metres after t seconds such that s=4t3-14t2+40t+8. a) When and where is the body momentarily at rest? b) For what time interval is it moving forward? c) During what times is its acceleration negative? d) Draw three separate graphs for acceleration, velocity, and displaceme

Curve Sketching

1. Draw a sign graph to determine where the following function is increasing or decreasing. Identify all stationary points. y=2x^4-4x^2+1 2. Find the intervals where the following curve is concave up or down. Also find the coordinates of any points of inflection. y=2x^3 - x^2 +3x+5 3

Comparing Equations of Lines

1.For the pairs of lines defined by the following equations indicate with an "I" if they are identical, a "P" if they are distinct but parallel, an "N" (for "normal") if they are perpendicular, and a "G" (for "general") if they are neither parallel nor perpendicular. 3x + 4y + 5 = 0 and y = - 3 4 x - 54 . x = 2 and y = p

Vectors : Linear Combinations and Spans

Please see the attached file for the fully formatted problems. 1) Determine if b is a linear combination of , . 2) List five vectors in span { }. For each vector, show the weights on used to generate the vector and list the three entries of the vector. Do not make a sketch. a) b) 3) Let For what

Critical Points

Let f(x,y)=((x^(2)y^(2))/(x^(2)+y^(2))), classify the behavior of f near the critical point (0,0).

Graphs : Hyperbolas and Parabolas

Given the graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. See attached file for full problem description.

Slope Predictor Formula : Finding a Tangent Line to a Curve

1. Apply the slope-predictor formula to find the slope of the line tangent to y = f(x) = (2x+4)2 - (2x-4)2. Then write the equation of the line tangent to the graph of f at the point (3, f(3)). My attempt... I found y first by: f(x) = (2x+4)2 - (2x-4)2 f(x) = (4x2+16x+16) - (4x2-16x+16) f(x) = (4x2+16x+16) + (-4x2+

Square root equations

Solve the following equations and show your work: 1) sqrt of x - 2 = 1 2) sqrt of x^3 = 27 3) 3 sqrt of x^2 = 9 4) Is (sqrt of x)^2 an identity (true for all nonnegative values of x)? x -2 -1 0 1 2 y .111 .333 1 3 9 Given the table above, graph the function, identify the graph of the function (line, parabol

Solving Linear Equations Word Problems

Section 3.1 # 94 Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is $5.00 per can. After experimenting with the prices for some time. Helen has determined that the weekly demand can be found by using the equation D=600-40p, Where d is the number of cans and p is the

Solving and Graphing Linear Equations and Word Problems

Week 3 Discussion Questions-Linear Equations in 2 Variables 1. Paul and nine other students are taking a math class. He is worried about the content of the next quiz because he just can't solve those word problems. The teacher has said that the number of questions divided by the number of students = 2.8, and 14.3 % of the tes

Y=x^2-6x+8 in to the form y=a(x-h)^2+k

Y=x^2-6x+8 in to the form y=a(x-h)^2+k How do you change the function? This initial problem is followed by: a) What is the equation for the line of symmetry for the graph of the function. (I think I can solve this ) Please explain and show in detail how to break this down in (dummy language) b) Asks that the functi

IP unit 1: Algebra Questions - Graphing, Domain, Range, Slope

1) a) Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. Graph Type: Explantation: Domain: Range: b) Given the above graph, identify the gr

Fixed Point Iterations

1. The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0 < A < B. (You do not have to show this.) (a) Show that A is in [0.5,0.7], and B is in [8.3,8.5]. (b) Consider the following fixed-point iteration for finding a solution of the given equation: xn+1 = e(1/3(Xn-2)): Show that if X0 = B+ E, where E is

Using a Graph to find the Maximum Area Enclosed; Volume Calculations

A rancher is building a rectangular corral and is using one wall of his barn as one of the sides. Because the barn wall is quite long, he needs fencing only along the other three He has 500 feet of fencing. The rancher wants the area of the conal to be as large as possible. should he choose as the dimensions of the corral? (Don'

Increasing function on open interval

Prove that if f is an increasing real-valued function on an open interval (a, b), then, for all but at most countably many points c in (a, b), Lim_(x-->c) f(x) exists and is equal to f(c).