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# Graphs and Functions

### Variables and Objective Function

A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is \$6.00 and the price per unit of the Illinois corn is \$5.50. a. Define variables that would tell how many units to purchase from each source b. Develop an objective function that

### Line graphs

1. Graph the equation by plotting points y = -2x 2. Graph the equation by plotting points. y = -3x 3. Graph the equation by plotting points. y = x - 3 4. Graph the equation by plotting points. y = x + 3 5. Use the following equation. Fill in the table. Determine whether the graph has a positive o

### Graph and rate of change of a function y=100(1.5^x)

Given the exponential function; y=100(1.5)^x, determine by the numerical method the average rate of change by calculating the slope at several arbitrarily chosen points shown below. a) Construct the data set and compute values of y for x=0, 1, 2, 3, 4, 5. Graph the function over these x values and explain in your own words wh

### Cost structure for a Radiologist group practice

Assume that a radiologist group practice has the following cost structure: Fixed costs \$500,000 Variable cost per procedure \$25 Charge (revenue) per procedure \$100 Assume that the group expects to perform 7,500 procedures in the coming year. a. Construct the group's base case projec

### horizontal line test

Consider the following function f: R R defined by f(x) = x3 - 8 . (a) Note the contrapositive of the definition of one-to-one function given on page 136 of the text is: if a b then f(a) f(b). As we know, the contrapositive is equivalent to, (another way of saying) the definition of one-to-one. Use

### Stem and Leaf plot

The number of surferââ?¬â?¢s special burritos served was sampled during a lunch period 11:00 a.m. ââ?¬" 2:30 p.m. at a taco shop on a weekday. Below is the sample: 41 63 39 56 46 55 38 66 41 48 60 57 48 31 71 56 60 39 52 Construct a stem and leaf plot of t

### Indexed Families of Sets

Describe each of the following as an indexed family of sets. Here, pi denotes the coordinated xy-plane. a) The family of closed intervals of length 1 on the real line. b) The family of all circles in pi of radius 1 whose center is on the y-axis. c) The family of all circles in pi of radius 1. d) The family of all li

### Functions: One-to-One Mappings

Let A = {a, b, c, d} and the set B = { 1, 2, 3} (a) How many functions are there from the set A to the set B. Explain. (b) How many 1-to-1 functions are there from the set A to the set B. Explain

### 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

### Fixed Point Theorem (using the Mean Value Theorem)

Prove that if f is a differentiable function with f´(x) > 1 for all x, then there is at most one c such that f(c) = c. [Use the Mean Value Theorem]

### Functions are investigated.

1. Evaluate the function f(x) = 9x - 6 for x=0. 2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost? 3. Find the slope of the line th

### 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