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# Graphs and Functions

### 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.

### Graphing Functiuons with Absolute Values

Graph each absolute value function and state its domain and range. See attached file for full problem description. y=|x-1| + 2

### Index of a Series, Functions, Arithmetic and Geomteric Sequences

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

### Parabolas : Concave up or Concave Down?

Determine whether the graph of the parabola opens upward or downward. See attached file for full problem description.

### Parabolas : Concave Up and Concave Down

What does a parabola open upward and when does it open downward? Please give an example.

### 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

### Graphing

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

### Tournament vertices

Show that if two vertices u and v have the same score in a tournament T, then u and v belong to the same strong component of T. Can you explain what does score mean? Hint : Try to prove it on two lines. Definitely your proof shouldn't be longer than 4 lines! If it is longer, you are doing something wrong.

### 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, Radicals and Rational Exponents

See attached file for full problem description. 1) Solve the following equations. a) Answer: Show work in this space. b) Answer: Show work in this space. c) Answer: Show work in this space. 2) Is an identity (true for all nonnegative values of x)? Answer: Expla

### 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

### Identify the graph of the function

See attached file for full problem description. 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.

### 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

### Solving Equations, Inequalities, Word Problems and Absolute Values (15 Problems)

1. Solve for x: 0.05(x+20)=0.1x-0.5 2. Solve for y, given that x = -3 3xy-2x=-12 3. Line 1 is described by the equation 3y-2x = -3. Line 2 goes through the origin and intersects line 1 at x =6. What equation describes line 2? 4. Solve for x: l x-1/2 l = 3x/2-3/4 5. Bob received \$14,000 inheritance and divided it b

### Four-Step Process to Find a Slope Predictor Function

Given f(x) = 2/(x-1) use the four step process to find a slope-predictor function m (x). Then write an equation for the line tangent to the curve at the point x = 0.

### 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

### Relations and Functions

In the real world, what might be a situation where it is preferable for the data to form a relation but not a function? There is a formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. You are given the following data points: Fahrenheit Celsius Freezing point of water 32 0 Boil

### 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

### Self-Complementary Graph Proof

1.10 Let G be a self-complementary graph of order n, where n=1(mod 4) Prove that G contains at least one vertex of degree (n-1)/2 (hint: Prove the stronger result that G contains an odd number of vertices of degree (n-1)/2. Can you explain it step by step and draw a graph.

### Graph positive vertices

1.2 Let n be a given positive integer, and let r and s be nonnegative integers such that r+s=n and s is even . Show that there exists a graph G of order n having r even vertices and s odd vertices.

### 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

### Connectivity for K-Partite Graph

3.16 Determine the connectivity and edge-connectivity of each complete k-partite graph. Can you explain it step by step and draw a graph.

### 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.

### Finding the Equation of the Tangent Plane to a Parametric Surface

Find an equation of the tangent plane to the parametric surface x = 5rcos(theta), y = 3rsin(theta), z = rat the point (5sqrt(2), 3 sqrt(2), 2) where r = 2 and theta = pi/4.