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Graphs and Functions

Graph Theory -Tree and Tree Structures

Trees can be used for many applications in computer science. One of these applications is decision-making, which is often used in the creation and analysis of databases. a) In one paragraph, define what trees are. Be sure to mention the difference between binary and n-ary trees. b) Represent the following hierarchical data

Relations and Graph Theory

1. Create a Binary Relation between X and Y that contains at least 6 Ordered Pairs, given that X and Y are the following: Let the set X = {Bill Smith, Amos Black, Tarra Sigorney, Alfred Ross} Let the set Y = {MAT 102, ENG 202. PSY 303, BUS 405} 2. Given the following information, create the appropriate Digraph Let X =

Determining the Limit of a Function

For the function f whose graph is given (attached), state the value of each quantity, if it exists. If it does not exist, explain why. (a) lim (x->0) f(x) (b) lim (x->3-) f(x) (c) lim (x->3+) f(x) (d) lim (x->3) f(x) (e) f(3)

The rational function

Let R(t) be the field of rational functions. Answer the following (with proofs): A. If we identify the rational numbers with a subset of R(t), what function corresponds to a given rational number r? B. Find a function f>0 in R(t) for which no rational number r satisfies 0 < r < f.

Slopes and intercepts and equations

1. Find the slope of the line. 5y-4x+2=0 2.A line passes through the point (x,y) = (-2,-1) and has a slope of -2 . Write an equation for this line. 3. Write equations for the vertical and the horizontal lines passing through the point (-2,0) in (x,y)-coordinates vertical line= horizontal line= 4.Find the values of

Graph of a linear function.

The manager of a weekend flea market knows from past experience that if he charges x dollars for a rental space at the flea market, then the number y of spaces he can rent is given by the equation y = 200 - 4x. (a) Sketch a graph of this linear function. (Remember that the rental charge per space and the number of spaces rented

A linear function problem

The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi. (a) Express the monthly cost C as a function of the distance driven d, assuming that a linear relationship gives a suitable model. (b) Use part (a) to

Functions and Graphs Evaluation

1. Evaluate the difference quotient for the given function. Simplify your answer. (1) f(x)=x^3, f(3+h) - f(3)/h 2. Find the domain and sketch the graph of the given functions: a. F(x) = 1/2 (x+3) b. f(x) = {-1 if x< or equal to -1 3x+2 if abs(x)< 1 7-2x if x > or equal to 1

Solving problems involving real data using Algebraic Concept

Using algebraic concepts to solve problems involving real data. World Population: A low-projection scenario of world population for the years 1995-2150 by the United Nations is given the function ... Flight of a Ball If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high ... S

Determining if the Points are on the Same Line

Indicate whether the given points below are on line 1, on line 2, on both line 1 and line 2, or on neither one of the two lines: Line 1: -4x -y+3=0 Line 2: 4x +3y -1=0 (x,y).............Line 1...........Line 2.........Both Lines..........Neither Line ( 1,-1) (2,-5) (4, 6)

Slope and intercept.

Part 1...Find the slope and y intercept for the line if there is a slope and y intercept. x+2y=3 Determine whether the lines are parallel, perpendicular, or neither. y=x+7 y=-x+2

Demand Function Problem

1.The demand function is: D(q) = 300/[4q+3] per unit. Find the total mount of money consumers are willing to spend to get 10 units of the commodity. 2. p= S(q) is the price (dollars per unit) at which q units of a particular commodity will be supplied to the market by producers, and q0 is a specified level of production. Fi

Graphing Software/Method

In our Learning-Team forum, we are to chose a graphing software/method and 'teach' it to the rest of the class. For this assignment, I have chosen the graphing software "Graph 4.x". As part of this assignment, we are to show how to start it, set it up, and how to graph functions (including parabolas and inequalities of 2 variabl

Trend Equation Contributors

The number of new contributors to a public radio station's annual fund drive over the last ten years is 63, 58, 61, 72, 98, 103, 121, 147, 163, 198 Develop a trend equation for this information, and use it to predict next year's number of new contributors.

Correlation/Linear Regression Guidelines

1. Construct a scatter plot using excel for the given data. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation. Complete the table and find the correlation coefficient r. a. The data below are the ages and systolic blood pressure (measured in millimeters of mercury

equation of the trend line

The average SAT verbal score for students from one high school over the last ten exams is 508, 490, 502, 505, 493, 506, 492, 490, 503, 501 Write the equation of the trend line. Do the scores support an increasing or a decreasing trend?

Plot graph of the equations

2. Plot the graph of the equations 4x - 6y = 12 and x - 5y = 10 and interpret the result. 3. Plot the graph of the equations 8x - 4y = 12 and -4x + 2y = -6 and interpret the result. Figured out the other graphs these two just arent looking right. Not sure if I figured the equations out right with the methods used.

Different Problems

Week 4/2 Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: 1. Integers 2. Rational numbers 3. Irrational numbers Week 4/ 3 1. How many solutions exist for a quadratic equation? How do we determine algebraically whether the solutions are real or complex? 2. Wh

Graph basic functions of one variable.

A. Given f(x) = -3x + 7 1. Graph f(x). 2. Label the graph. B. Given f(x) = -3x2 + x - 5 1. Graph f(x). 2. Label the graph. Note: To draw the graph, you may use one or a combination of the following: - A spreadsheet program, such as Excel (*.xls) - A graphics program, such as Paint (*.jpeg, *.gif) - A word

Linear programming: Constrained optimization problem

A business student at Nowledge College must complete a total of 65 courses to graduate. The number of business courses must be greater than or equal to 23. The number of non-business classes must be greater than or equal to 20. the average business course requires a textbook costing $60 and 120 hours of study. Non-business cours

Functions : Trnslation, Domains and Asymptotes

Please see the attached file for the fully formatted problems. MTH133 Name: 1) State the domain of the following and provide a brief explanation for your answer: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the followi

Slope of a Line Equation

1. If line / goes through (1,3) and is parallel to the line through (4,3) and (-3,1). find the slope of /. 2. How do I write the equation y=2/3x-3 in standard form using only integers and a positive coefficient for x. 3. What is the equation if a line /goes through (-3,-1) and (-1,4)? 4. What is the equation in slo

Slope and Intercept

Need to provide a real world situation where the slope and intercept have some meaning in reality. The situation needs to describe what the dependent and independent variables are and what the slope and intercept means in terms of the real parameters.

Rational Functions and Polynomials

Explain what makes a function a polynomial. Give an example of a function that is a polynomial and a function that is not a polynomial. Given the polynomial f(x) = 2x3 + 5x2 - x - 5, answer the following questions: Graph the polynomial. What is the degree of the polynomial? Explain the constant in the polynomial and how

Finding the range of the selling price

Need assistance in solving this problem using inequality: Joe wants to sell his car through a broker who charges a commission of 10% of the selling price. Joe still owes $11,025 on the car. Joe must get enough to at least pay off the loan. What is the range of the selling price?

Explain what is meant by a function.

1. Explain what is meant by a function. Give two real-world examples of relationships that are functions and two real-world examples that are not functions. 2. How many x-intercepts can a function have? Give a specific example and state the rule that backs up your answer. 3. Explain how the vertical line test works t

Functions, Graph and Equations