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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

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)

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

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.


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

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.

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 +

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?


1. State the key features (vertex, focus, directrix, direction of opening, and axis of symmetry) of each parabola, and sketch the graph. a) ysquared-2x+4y-7=0 2. Find the equation of each parabola. a) parabola with focus (-2,-1) and directrix y=5 b) ysquared=-6x translated according to ((x,y)arrow(x-2, y+4)

Find the interval on which the function

See attached file for full problem description. Find the interval on which the function 2 2 ( ) ( 2) ( 3) f x x x = &#8722; + is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.