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# Graphs and Functions

### Various Algebra Problems

See attached file for full problem description. 1. Find the missing coordinates in the following table: 2. Graph the following equation. Plot at least five points for the equation: x + 4y = 5 3. Demand Equation. Helen's Health Foods usually sells 400 cans of Pro Pac Muscle Punch per week when the price is \$5 per can. Af

### Writing an Equation as a Function of X

-3x+4y=11 I am trying to rewrite this as a function of x.

### Complete the ordered pair .

F(x) = x^2 + 7x +7, (4, )

### Justifying An Increased Line of Credit

Case 3: Justifying An Increased Line of Credit 1. A monthly regression analysis is to be conducted using monthly data for each demand variable. Formulate your empirical model using the additive functional form. 2. Using economic theory what are the hypothesized signs of parameters in the demand model. 3. Interpret your

### Linear Equations, Midpoints and Distance Between Two Points

6. Consider the points (4, -1) and (7, 8). (a) Find the midpoint of the line segment with the given endpoints. (b) Find the distance between the points. Give an exact answer (simplified as much as possible), and also an approximation to three decimal places. Show some work. (c) Find the slope of the line passing through the

### Comparing plots on graphs for a linear equation

You are the financial manager of a furniture company. It is your job to create supply and demand graphs that show the break-even point for the company. The functions that describe how the company can break even will be represented with linear equations. Linear inequalities will be used to graph conditions where the company exper

### Arithmetic and Geometric Series

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

### Equivalence relations, surjective maps, partitions and fibers.

Consider any surjective map f from a set X onto another set Y. We can define a relation on X by x_1 ~ x_2 if f(x_1) = f(x_2). Check that this is an equivalence relation. Show that the associated partition of X is the partition into "fibers" f^(-1) (y) for y in Y. I would like to understand what this question is asking me a

### Monte Carlo Methods : Cumulative Density Function

Show that if the value of a variable x is selected by inverting the cdf (cumulative density function), x = F^-1 (RN), the distribution of the x values is given by the function f(x). See attached file for full problem description.

### Graph Theory, Necessary and sufficient condition digraphs to be Eulerian.

Page 90, Theorem 4.6 ( To show that a digraph is hamiltonian if and only if for each vertex v, indegree (v) =outdegree (v) Page 92 Exercise problem 4.1 ( A modified version of konigsberg problem where, two extra bridges are built. ) Page 93, Figure 4.5 need to show as Hamilton. (Show that dodecahedron is hami

### Evaluating and Graphing Functions and Trigonometry Word Problems

(1) For the function: (see attached) a) Give the y values for x = -1, 0, 1, 2, 3, 4. b) Using these points, draw a curve. (2) For the equation , perform the following: (a) Solve for all values of x that satisfies the equation. (b) Graph the functions y = x and on the same graph (by plotting points if necessary). Sho

(1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: (a) Solve by factoring. (b)Solve by using the quadratic formula. (2) For the function y = x2 - 6x + 8, perform the following tasks: (a) Put the function in the form y = a(x - h)2 + k. (b) What is the equation for the line of symmetry for t

### Graphing Linear Equations an Geometry of Coordinate Points

Please see the attached file for the fully formatted problems. Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept 1. Slope: -2; y-intercept: (0, 4) 2. Slope: 5; y-intercept: (0, -2) 3. Slope: ; y-intercept: (0, 8) 4. Find the slope of any line pe

### Give an example of a real life situation for each graph.

All of the graphs in occur in real life. Find a real-life application of each of the below graph and describe the characteristics of each application as related to the graph. line parabola hyperbola exponential

### Graphing Linear Equations Word Problems

A bus company in a small town has an average number of riders of 800 per day. The bus company charges \$2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each \$.25 increase in fare. 2) If the number of riders are a function of the fare charged. Gr

### Derivatives and Rate of Change Word Problems: Motion and Relative Speed

1.A body has an a equation of motion measured in metres after t seconds such that s=4t3-14t2+40t+8. a) When and where is the body momentarily at rest? b) For what time interval is it moving forward? c) During what times is its acceleration negative? d) Draw three separate graphs for acceleration, velocity, and displaceme

### Sample Question: Equation of a line

Find the equation of the line shown: Please see the attached file for the fully formatted problems.

### Curve Sketching

1. Draw a sign graph to determine where the following function is increasing or decreasing. Identify all stationary points. y=2x^4-4x^2+1 2. Find the intervals where the following curve is concave up or down. Also find the coordinates of any points of inflection. y=2x^3 - x^2 +3x+5 3

### Slope Fields

Suppose the constant function y(t) = 2 for all t is a solution of the differential equation dy = f(t,y). dt (a) What does this tell you about the function f(t,y)? (b) What does this tell you about the slope field? In other words, how much of the slope field can you sketch using this information? (c) What does this

### Maximizing the Volume of an Open Top Box by Graphing

An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function and

### Relations and Functions; Celsius / Fahrenheit Temperature Conversions

#1: 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 Cels

### Problem on R-chart

Attached is an R chart in Excel. Plastics food containers that can be baked in ovens must be able to withstand certain temperatures without melting. One such container, which is 4 inches deep, is designed for use at oven temperatures of 325°F. To monitor the quality of these containers, a subgroup of 5 finished containers i

### In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?

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

### Find the slope and find the intersection

1. Find the slope of the line 2x + y = 4. 2. Find the point of intersection of the lines x + y = 5 and 3x - y = 7. Graph the pair of lines.

### Comparing Equations of Lines

1.For the pairs of lines defined by the following equations indicate with an "I" if they are identical, a "P" if they are distinct but parallel, an "N" (for "normal") if they are perpendicular, and a "G" (for "general") if they are neither parallel nor perpendicular. 3x + 4y + 5 = 0 and y = - 3 4 x - 54 . x = 2 and y = p

### Vectors : Linear Combinations and Spans

Please see the attached file for the fully formatted problems. 1) Determine if b is a linear combination of , . 2) List five vectors in span { }. For each vector, show the weights on used to generate the vector and list the three entries of the vector. Do not make a sketch. a) b) 3) Let For what

### Critical Points

Let f(x,y)=((x^(2)y^(2))/(x^(2)+y^(2))), classify the behavior of f near the critical point (0,0).

### Graphs : Hyperbolas and Parabolas

Given the graph, 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. See attached file for full problem description.

### Crate's weight perpendicular and parallel to the incline

The chemical retardants are freight shipped from a warehouse. A shipping crate that weights 450 kilograms is placed on a loading ramp that makes an angle of 30 degrees with the horizontal. Find the magnitude of the components of the crate's weight perpendicular and parallel to the incline.

### Graph each function using Microsoft Excel and state its domain and range.

Graph each function using Microsoft Excel and state its domain and range. g(x) = x+2