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Graphs and Functions

Proof of N-Vertex Simple Graph

Prove or disprove: a. There exist a connected n-vertex simple graph with n+1 edges that contains exactly two cycles. b. There does not exist a connected n-vertex simple graph with n+2 edges that contains four edge-disjoint cycles.

Using the demand function to write cost and revenue functions

A health club has cost and revenue functions given by C = 10,000 + 35q and R = pq, where q is the number of annual club members and p is the prices of a one year membership. The demand function for the club is q = 3000 - 20q. a. Use the demand function to write cost and revenue functions of p. b. Graph cost and revenue as

Linear Equations / Graphs / Slopes

please show your work. 1. Use the equation below and the indicated value to find an ordered pair that is a solution. y = 2x - 1 let x = 6 2. Complete the table of values for the equation 6x + 2y = 72. 3. Decide whether the ordered pair (9,5) is a solution of the equation. x + y = 9 4. Find the value of the expressio

Basic slope intercept equations are examined.

. Determine whether the relation is a function. {(-2, -7), (3, -5), (6, -4), (9, -6), (10, -1)} A) Not a function B) Function 2. Determine whether the relation is a function. {(-5, -4), (-2, 9), (-1, -2), (-1, 7)} A) Function B) Not a function 3. Determine whether the relation is a function. {(-7, -1), (-7, 2), (-

Graphs and Plots of Linear Equations

3. Graph by plotting points. y+x= -4 4. Graph by plotting points. 3x= -y+3 Complete the ordered pairs. (-1,_), (1,_) 6. Find the intercepts for the graph of the equation given. x+4y=0 the x-intercept is? the y-intercept is? 7. Find the intercepts and then use them to graph the equation.

Applying graph theory

Let G be a simple graph on n (greater or equal then) 3 vertices such that deg_G(v) (greater or equal to) n/2 for every vertex v E V(G). Prove that deleting any vertex of G results in a connected graph (i.e. G is 2-connected).

The relationship between points and a line

By a line, a great circle on the sphere is referenced. Is it still true that two points determine a unique line? Is it still true that two distinct lines either meet in a single point or do not meet at all? Explain.

Intercepts, substitutions and graphs

1. y = 2x + 3 and y = -x - 4 2. 2x + 3y = 8 and 3x + 2y = 7 3. x + y = 3 and y = x + 3 4. A university bookstore recently sold a wirebound graph-paper notebook for $2.50, and a college-ruled notebook for $2.30. At the start of spring semester, a combination of 50 of these notebooks were sold for a total of $11

Solve systems of equations with two and three variables.

Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong. 1. Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6 2. Alice's Restaurant has a total of 205 seats. The n

Systems of linear Equations

Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong. 1. Determine whether the lines will be perpendicular when graphed. 3x - 2y = 6 2x + 3y = 6 2. Alice's Restaurant has a total of 205 seats. The n

Tree Diagram and Probability

A min license plate for a toy car must consist of a one digit odd number followed by two letters . each letter must be a J or K. Repetition of letter is permitted. Use the counting princdiple to determine the number of points in the sample space. Construct a tree diagram to represent this sitution. list the sample spa

Finding the Exact Area Under a Graph

** Please see the attached file for a Word formatted copy of the problem description ** 1. let f(x) = x^2-2x+2 on the interval [-1, 2]. Sketch a graph of this function along with the rectangles that would be used to approximate the area under the curve using a right sum with n = 6. Be accurate and make your graph large. a) C

Graphing help is achieved.

1) The following graph shows the depreciation for the corporate airplane from 2006 to 2009. The plane was purchased new in 2006; therefore, x = 0 represents the year 2006. X â?" axis (horizontal) = years starting from 0 = 2006 and increasing by 0.5 years Y â?" axis (vertical) = price in $ amounts from 24,000 to 240,000

Functions and Equations

1. Evaluate the function f(x) = 4x + 6 for x=4. 2. Evaluate the function f(x) = 9x - 6 for x=0. 3. Take a look at the following table: x -2 -1 0 1 2 f(x) -5 -2 1 4 7 a. Write out an equation for f(x). Assume the function is linear b. What is the slope? Is it negative or positive? What information do we ge

Explanation for parabolic equations

The surface of planet Xyz, in a galaxy far away is mostly an ocean of Nitric Acid. The planet is inhabited by two tribes of human-like creatures, the Blue People and the Green people, who live in separate islands. They know of each otherâ??s existence because they had a common origin, but because of the corrosive nature of th

Fixed cost and the variable cost

If we graph this data with Total Cost on the Y axis (Vertical axis) and the Quantity Produced on the X axis (Horizontal axis) what do you think will be the shape of the line and how can we determine the Fixed Cost and the Variable Cost/Unit from that graph?

Largest Domain of the Function

Consider the function f(x) = arcsin(1 - x^2). (a) What is the largest domain over which this function is defined? (b) For this domain, what is the corresponding range of the function? (c) If this function is one-to-one, find the inverse function f^-1(x), and state the domain of this inverse function. Otherwise, find a suitabl

Graphing of Function With Vertical & Oblique Asymptotes

1. When preparing to graph the rational function y(x), this algebra is done. (a) Specify, with reasons, the (largest) domain of y(x). (You needn't repeat algebra) (b) Find where the graph crosses the y-axis. y(x) = x^4 - 2x^3 - 3x^2 - 3x â?" 1 x^3 - 3x^2 + x - 3 = x + 1 -(x - 1)(x + 2) (x - 3)(x^2 + 1) = x + 1 â?" 1

Function of Variable Evaluated

What is a function, in your own words? Give an example of a function using the variable x and explain how we evaluate a function for a given value of x.

Mapping is assessed.

Given: All students at a university have a mentor. A. Explain why the given described is an onto mapping. B. Create a own real-world example of an onto mapping without using a math formula o Explain what set constitutes the domain. o Explain what set constitutes the codomain. o Explain what relationship exists betwe

Graphing and Finding Area

Graph the function f(x) = cos2 x on the interval [-π, π], showing the addition of the rectangles associated with the Riemann sum Σ f(ck)Δxk given that ck is the midpoint of the kth subinterval from k = 1 to 4.

How to decide whether to take mean, median, mode, or range?

For each of the following data sets, select the best measure of central tendency, explain why your selection is the best measure, and then compute that measure of central tendency for the data. 1. Approximate average household incomes for families that live in the Fallen Pines subdivision (in thousands of dollars: 55, 59, 39,

Function of Weight of the Rocket

A rocket burns up to 3 tons/ min after falling out of orbit into the atmoshpere. If the rocket weighed 5,200 tons before reentry express in weight w as a function of the time t, in minutes of renentry Write the weight of the rocket as the function w(t)

the maximum or minimum value of the quadratic function

Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function. f(x)= -2^2 + 2x + 4 x- coordinate of the vertex is ______ y- coordinate of the vertex is _______ The equation of the line of symmetry is _______ The maximum/minimum of f(x) is________

Math: Elimination and substitution methods

Explain what the domain and range are of a function. Next, select an exercise between 13 and 36, inclusively, on pages 500 -501 of section 7.2. Find the domain of your selected function while showing your work, and explain the process. f(x)=2x+1 Show how to solve it using the substitution method, and explain this proces

Express equation in slope intercept form.

In the problem below, assume that the relationship can be expressed as a linear equation in two variables, and use the given information to determine the equation. Express the equation in slope-intercept form. A new diet fad claims that a person weighing 160 pounds should consume 1620 daily calories and that a 200 pound pers

Quadratic Minimum Maximum Problems

A rope connects two poles that are 80 feet apart. The function .02x^2+15 models the height the rope is above the ground. a. graph the function b. what is the minimum height? c. what is the maximum height?

Functions and Models

Think of a mathematical function that represents something from your own life. For example, suppose the number of beers you drink depends on the number of football games you watch. If you drink five beers during every football game, the function would be: Number of Beers (B) = 5 times Number of Football Games (F), or B = 5F

Reciprocal Function Overview

The Rule of 70 is a mathematical approximation that calculates how long it takes for a value to double. Examples are as varied as finding how long it takes the Gross Domestic Product to double, how long it takes a savings account to double in value, or how long it takes the price of a product to double due to inflation. The Rule

Hyperbola graphs to determine foci and vertices

I need to graph the following hyperbola and it has been several years since I have done this. Can you give me a step by step method of how to do this? x^2 = 8(y-1)^2+1 I do not remember how to determine the foci or the vertices. Please assume that I know nothing other than the given equation. Once I know the method I will