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Graphs and Functions

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).

Vertex, Focus and Directrix of Parabola and Ellipse

1. Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. 2. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled. 3. Find the equation of the ellipse whose center is the origin and has a

Mappings, Injective and Surjective Functions and Cycles

1. Let f : X -> Y and g : Y -> Z be mappings. (1) Show that if f and g are both injective, then so is g o f : X -> Z (2) Show that if f and g are both surjective, then so is g o f : X -> Z. 2. Let alpha = 1 2 3 4 5 and Beta = 1 2 3 4 5 3 5 1 2 4 3 2 4 5 1 .

How do you use linear equation in business?

In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approxima

Petersen Graph Nonplanar

Show that the Petersen graph is nonplanar by a) showing that it has k3,3 as a subcontraction, and b) using the problem 1 show above part a) You don't have to solve problem 1. Can you explain about contraction. problem 1.-Let k>=3 be an integer , and let G be a plane graph of order n(>=k) and size m. a) If the length

Trees and Graphs : Outerplanar Graphs

What bound is given for X(G) by the theorem "for every graph G, X(G)<=1+max &(G') ,where the maximum is taken over all induced subgraphs G' of G" in the case that G is a) a tree? b) an outerplanar graph. Note: -&(G') this sign represent the minimum degree of G'. Yes it is that minimum -A graph G is outerplana

Calculating Work and Slope of a Tangent

1. The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm? Hooke's law for a spring is given by f=kx, where f is the force, x is the distance the spring is stretched, and k is a constant. 2.

Finding domain & range

Finding domain & range. See attached file for full problem description. (a) f(x) = (x -2)/ (3x + 4) (b) g(x) = -11/(4 +x) (c) g(x) = 4x^3 + 5x^2 -2x

Evaluating Functions and Applications of Functions

7.1 Determine whether the correspondence is a function. 8. Domain Range Colorado State University University of Colorado ____________ > Colorado All three colleges points to college University of Denver Gonzaga University University of Washin

Graphing and Solving Linear Equations

Graph and, if possible, determine the slope. Graph using the slope and the y -intercept. Determine whether the graphs of the given pair of lines are parallel. Determine whether the graphs of the given pair of lines are perpendicular. See attached file for full problem description. 7.4 Graph and, if possible, determi


Please see the attached file for the fully formatted problems.

Graphing Slopes - Constant of Proportionality Best Compensate

When crude oil flows from a well, water is frequently mixed with it in an emulsion. To remove the water the crude oil is piped to a device called a heater-treater, which is simply a large tank in which the oil is warmed and the water is allowed to settle out. Operating experience in a particular oil field indicates that the conc

How to graph a simple equation

Please help me graph the line with equation: y=-5x-4 Also, show all of the steps so that I can learn how to do it myself.

Sample Question: Graph

1. Plot the graph of the equations 2x - 3y = 6 and 2x + y = -10 and interpret the result. 2. Plot the graph of the equations 2x + 4y = 10 and 3x + 6y = 12 and interpret the result. 3. Determine graphically the vertices of the triangle, the equation of whose sides are given as y = x; y = 0; 2x + 3y = 10. Interpret the res

Graphing Linear Functions and Finding the Point of Intersection

A. The solutions of line m are (3,3),(5,5),(15,15),(34,34),(678,678), and (1234,1234). b. The solutions of line n are (3,-3),5,-5),(15,-15),(34,-34),(678,-678), and (1234,-1234). c. Form the equations of both the lines d. What are the co ordinates of the point of intersection of lines m and n? e. Write the co-ordinat

Hamiltonian Graphs and 2-Connected Graphs

Explain this problem with a graph to understand and explain it step by step. a) Show that if G is a 2-connected graph containing a vertex that is adjacent to at least three vertices of degree 2, then G is not hamiltonian. b) The subdivision graph S(G) of a graph G is that graph obtained from G by replacing each edge uv of

Hamiltonian and Nonhamiltonian Graphs

4.15 Show that this theorem 1 is sharp, that is, show that for infinitely many n>=3 there are non-hamiltonian graphs G of order n such that degu+degv>=n-1 for all distinct nonadjacent u and v. Can you explain this theorem,please Theorem1: If G is a graph of order n>=3 such that for all distinct nonadjacent vertices u and

Determining Order Quantity

At Dot Com, a large retailer of popular books, demand is constant at 32,000 books per year. The cost of placing an order to replenish stock is $10, and the annual cost of holding is $4 per book. Stock is received 5 working days after an order has been placed. No backordering is allowed. Assume 300 working days a year. a)What

Prove Let D be a nontrivial connected digraph.

4.4 Prove Let D be a nontrivial connected digraph. Then D is Eulerian if and only if od(v)=id(v) for every vertex v of D. Od means the outdegree of a vertex v of a digraph D. (is the number of vertices of D that are adjacent from v. id means the indegree of a vertex v of a digraph D.( is the number of vertices of D adjace

K-connected graph

3.17 Let v_1,v_2,...,v_k be k distinct vertices of a k-connected graph G. Let H be the graph formed from G by adding a new vertex of degree k that is adjacent to each of v_1,v_2,...,v_k. Show k(H)=k. k(G)=is the vertex connectivity

Intercepts of a Line

Find both the X-intercept and the Y-intercept of the line given by the equation - 9x + 4y + 13 = 0

A Nontrivial Connected Digraph

Prove that a nontrivial connected digraph D is Eulerian if and only if E(D) can be partitioned into subsets E_i , 1<=i<=k, where [E_i] is a cycle for each i. <= means less and equal. Please can you explain this step by step and can you draw a graph.