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Graphs and Functions


Please see the attached file for the fully formatted problems.

Graph the line

Graph the line with equation. See attached file for full problem description.

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

Inverse Functions and Set Operations

Let f be a function from A to B. Let S and T be subsets of B. Show that: a) -1 -1 -1 f (S U T) = f (s) U f (T) b) -1 -1 -1 f (S n T) = f (S) n f ( T)

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

Slope and Intercept

8. The slope and x-intercept of the line 4x + 6y + 24 = 0 are a) -2/3 and (-6, 0) b) -3/2 and (0, -4) c) -4 and (-24, 0) d) none of the above 9. The slope of the line passing through (1,1) and (1,-1) is a) 1 b) 0 c) 2 d) inf

Pade Approximation

Let f(x) = cos(x) = ; then, consider the following rational approximation r(x) = called the Pade Approximation. Determine the coefficients of r in such a way that f(x) - r(x) = γ8x8 + γ10x10 + ...... Please see the attached file for the fully formatted problems.

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

Hamiltonian Graphs

4.12 a) Prove that K_r,2r,3r is hamiltonian for every positive integer r. b) Prove that K_r,2r,3r+1 is hamiltonian for no positive integer r. (K_r means k sub r) Can you explain how is the graph K_r,2r,3r, what do subindices r,2r and 3r mean? Can you explain it step by step and draw a graph,plea

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

Graphing Line Equations

Graph the line with slope -3/4 through the pint (-5,-5) See attached file for full problem description.

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

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.

Strongly Regular Graph

Let n >= 2 be a number. Define the graph L2(n) as follows: Vertices are ordered pairs from the set {1, ..., n}. Two vertices are adjacent if they have the same first coordinate, or the same second coordinate (but not both). Show that this is a strongly regular graph, and find its parameters.

Find examples of four types of graphs.

Relate the application to the specific graph (line, parabola, hyperbola, exponential). Describe the characteristics of each application as related to the graph. All of the graphs in this lesson occur in real life. Using the Cybrary, web resources, and other course materials, find a real-life application of each graph. ? R