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# Graphs and Functions

### Find examples of four types of graphs.

Relate the application to the specific graph (line, parabola, hyperbola, exponential). Describe the characteristics of each application as related to the graph. All of the graphs in this lesson occur in real life. Using the Cybrary, web resources, and other course materials, find a real-life application of each graph. ? R

### Connected Graphs

Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G? Prove your findings! Let G be a connected graph and sq(G) be a graph which contains all vertices and edges of G and moreover edges joining every pair of vertices that were in G at distance 2. In other words, xy is

### Cancer and Heart Disease : Graphing, Trends and Forecasting

1. Disease 1985 1990 1995 2002 Heart Disease 771169 720058 737563 696,947 Cancer 461563 505322 538445 557,271 2. a. Plot this data for each disease as points in a rectangular coordinate system. b. Using a smooth line, connect your data points for each disease. c. On a separate graph, plot only the years

### Complement Graphs

(1) Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph. (Please read carefully the definition of an induced subgraph before you attempt to solve it!). Simple graph is a graph with no loops or multiple edges. K_1 is also a tree. (2) Let v be a c

### If we use the usual method of taking the right endpoint to be the height of each rectangle, then our approximation will be an

Suppose that f is an positive-valued, increasing function on the interval from x = 0 to x = 4, and that we use the method of rectangles to approximate the area between the curve and the x-axis. If we use the usual method of taking the right endpoint to be the height of each rectangle, then our approximation will be an _________

### Finding the Equation of a Line

Find the equation of the line through each given pair of points. Write the answer in standard form using only intergers. (3, 5), (8, 15)

### Write each equation in slope - intercept form.

Write each equation in slope - intercept form. 2x + 3y = 90

### Function Expressing Volume of a Cardboard Box

Please help with the following problem. Please provide step by step calculations for each. A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in. by 17 in. by cutting equal squares from the four corners and turning up the sides. (a) Find a mathematical model express

### For the set of scores calculate the requested values

1. For the set of scores calculate the requested values. Scores: 2 5 3 6 4 a.{X b.{x^2 c.({X)^2*5 2. For the set of scores calculate the requested values. X Y 8 -1 11 3 2 5 3 -4 a.{XY b.{X{Y ({XY)^2 d.{(x-1)^2{Y+3)^2

### Exponential and Radical Expressions Problem Set

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign. Please provide sources used. 1) Solve the following e

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 values of x)? Answer: Explain your answer in this space. 3) x -2 -1 0 1 2 y .25 .

### Inverse functions

Show both analytically and graphically that f and g are inverses: f(x) = 3-4x g(x) = (3-x)/4

### Construct a graph

(See attached file for full problem description) The function that describes first-class mail postage has discontinuities. The cost of first-class mail is 37¢ for the first ounce (or less) and then 23¢ for each additional ounce above that. Make a graph showing the total cost of postage for packages up to 4 ounces.

### Select best answer

(See attached file for full problem description)

### GRAPHS and COMPOUND INEQUALITY

I need to graph the solution set to each compound inequality. 1. x > - 2 and x < 4 (Please note that this symbol < is underlined) sorry I don't know how to do the underlining. I need to graph each compound inequality for this problem 2. 3 - x < y + 2 or x> y + 5

### Graphing and Solving Equations

1. Evaluate. (-8)2 - 19 A) 45 B) -83 C) -35 D) -45 2. Solve and graph the solution set. 4x + 9 &#61619; 3x + 16 A) -7 0 B) 0 7 C) -7 0 D) 0 7 3. An arithmetic student needs an average of 70 or more to receive credit for the course. She scored 67, 74, and 63 on the first three exams. Write

### Graphing functions with absolute values.

Graph each absolute value function and state its domain and range. Please see the attached file for the fully formatted problems.

### Functions : Determine whether the table expresses the second variable as a function of the first variable.

Determine whether the table expresses the second variable as a function of the first variable. Please help with attached problem.

### Collinear Points

1. Use the Concept of slope to find t such that the three points are collinear. 1)(1,-4),(t,3),(5,10) 2. Find an equation of the line that passes through the given point and has the specified slope, and find three additional points through which the line passes. 1)point:(2,-1) Slope:m=1/4 2)point:(0,-5) Slope:m=3/2 3.

### Find area of region bounded by graphs.

Problem: Sketch the region bounded by the graphs of: y = 9 - x2, y = 5 - 3x and then find its area.

### Find: The Domain and Range of a Function

Consider the following equation: X = y^2 - 1. Now, find the domain and range which accompanies the function.

### Solve: Graphing Functions

Please complete the following: Graph each function and state the domain and range: G(x) = x^2 - 2x - 15

### Determine the Largest Size N For Each Function

For each function f(n) and time t in the table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. Show all work in detail. (see chart in attached file)

### For each system of linear equations shown below...

For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent," and answer the question about its solutions. a) Line one y=2x+8 Line two y=-2x - 4 b) line one y=-2x+1 line two y= -2x+4 c) line one y= 1/3x-1 line two - x +

### To calculate the world grain demand be in 2010 and the range of the car selling price

1.WORLD GRAIN DEMAND Freeport McMoran projects that in 2010 world grain supply will be 1.8 trillion metric tons and the supply will be only 3/4 of world grain demand. What will world grain demand be in 2010? 2. CAR SELLING Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. R

### Graphing absolute value functions (domain and range).

Graph each absolute value function and state its domain and range. g(x) =|x| - 3

### Determine whether each table expresses the second variable as a function of the first variable.

Determine whether each table expresses the second variable as a function of the first variable. C h 345 0.3 350 0.4 355 0.5 360 0.6 365 0.7 370 0.8 389 0.9

### Using a Parabola: Maximum Height Reached by a Soccer Ball

If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t where t is time in seconds. Graph this parabola for 0 < or equal to t < or equal to 2. What is the maximum height reached by the ball?

### Use the product rule to find the slope of the line tangent to the graph of the function.

Use the product rule to find the slope of the line tangent to the graph of the function. f (x) = x^2 (1 + 3x3) at the point (1, 4)

### Find five numbers with a mean of 16, a median of 15, a mode of 21 and a range of 11.

Find five numbers with a mean of 16,a median of 15, a mode of 21 and a range of 11.