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Graphs and Functions

Find and label the vertex and the line of symmetry.

Don't mind the graphing part. What I got out of the assignment is the vertex portion. Please see the attached file. 1.Find and label the vertex and the line of symmetry. Graph the function. F(x)= 4x The vertex is (type an ordered pair) 2.Find and label the vertex and the kline of symmetry. Graph the function f(x)=(

Solving Equations and Word Problems

Please show work. Thanks! 1.Simplify -2c(c-8)-3(c-8) 2. Solve the equation x- .05x = 190 3. Solve the equation 5x -9 = x-4 4. Solve the equation system x + y = 5, x - y = 1 5. Gra

Explain vertical line with a graph of equation x = 4.

Why is the line x=4 a vertical line? A brief and an original writeup has been provided to explain the student community the concept of vertical lines. A graphical example of equation x=4 has been attached to aid the understanding of the concept.

Graphing Functions

To exercise your skills, you are to perform the following using different tools available to you (e.g. Excel spreadsheet, graphing calculator, etc.) and write and explanation on your findings: The graph of: f(x)= 0 The graph of: f(x) = a0 , where a0 ≠ 0 The graph of: f(x) = a0 + a1x , where a1 ≠ 0 For each o

Solving Equations and Inequalities

1. Simplify: (-4)(5)(-7)(2) 2. Two trains are approaching each other on the same track. They are 500 miles from each other. One train is traveling at 40 mph, the other at 60 mph. A bird is flying back and forth between them at 150 mph. How long before they collide? 3. Solve for y: x = (y-b) / m

An Application of a Rational Function

An application of a rational function is T = (AB)/(A+B), which gives the time, T, it takes for two workers to complete a particular task where A & B represent the time it would take for each individual worker to complete the identical task. Estimate how long it takes you to complete a task of your choice (house cleaning, mow

Vertical Asymtotes, Holes and Horizontal Asymtotes

For the rational function f(x)=[3x(x-1)]/[(x-1)(x+2)] a) Find each of these features, saying how you know in each case 1. Verticle asymptotes (if any) 2. Holes (if any) 3. Horizontal asymtotes (if any) b) Draw a neat graph of f(x), showing any asymptotes and/or holes appropriately.

Cost and Revenue Functions and Breaking Point

1. A company that manufactures bicycles has a fixed cost of $ 100,000. It costs $ 100 to produce each bicycle. The selling price per bike is $ 300. a) Write the cost function, C. b) Write the revenue function, R c) Determine the breaking point. Describes what this means.

Graphing, Slopes and Intercepts

1. Give an example of a linear function and show at least one method of graphing it. By looking at the graph of a line, how can you tell if its slope is negative? What kind of line has a slope of zero and why? 2. Give an example of quadratic function and show at least one method of graphing it

Functions : Domains, Transformations and Asymptotes

MTH133 Unit 5 Individual Project - A Name: 1) Find the domain of the following: a) Answer: Explain how you obtained your answer here: b) Answer: Show your work or explain how you obtained your answer here: c) Answer: Explain how you obtained your answer here: d) Answer: S

Domain and Range of a Function..

1 Use the graph to find a reasonable estimate of f(-2). Graph is included in the attached document. 2 What is the domain of f (x) 3 What is the range of f (x) 4 Explain why f represents the graph of a function

Two applications of a rational functions

Part 1: An application of a rational function is Young's rule, which approximates the dosage of a drug prescribed for children. a) Using the Library, web resources, and/or other materials, find the equation for Young's rule. State what each variable in the equation represents. Do not type the equation using the Equatio

Graphs and Systems of Inequalities

11. Match the graph with one of the equations. a) y = x b) y = 3x c) y = d) y = x + 3 14. A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours. The labor available is limited to 80 hours per week, and the total production

Equation of a Tangent Line

Write an eq. of the line tangent to the curve y = (5/x2) - (2/x3) at the point P(-1,7)? Express in ax+by=c form.

Find a real-life application of a linear function.

Part 2: Using the Library, web resources, and/or other materials, find a real-life application of a linear function. State the application, give the equation of the linear function, and state what the x and y in the application represent. Choose at least two values of x to input into your function and find the corresponding y fo

Graph the parabola

Please assist with the attached problem. y = -1/4x^2 + x - 6 Identify the vertex and four additional points on each side of the vertex

Find the slope and y-intercept

Please see attached file. Name: __________________________ Date: _____________ 1. Find the slope and y-intercept. x = -7 A) Slope: undefined; y-intercept: (0, -7) B) Slope: 0; y-intercept: none C) Slope: undefined; y-intercept: none D) Slope: 0; y-intercept: (0, -7) 2. Match the graph with one of the equation

Find the slope of any line perpendicular to the line through points

16. Find the slope of any line perpendicular to the line through points (0, 5) and (-3, -4). 20. on page 626 27. Geometry. Floor plans for a building have the four corners of a room located at the points (2, 3), (11, 6), (_3, 18), and (8, 21). Determine whether the side through the points (2, 3) and (11, 6) is parallel to


28. x + y = 18 24. 3x _ 4y _ 12 (0, ) (0, ), , ( , 0), 26. y=2x + 5 (0, ), ( , 5),( ), ( , 1) 28. x + y = 18 Give the coordinates of the points graphed below ( I couldn't load the graph, but it wanted o show the points) 2. B 4. D 23.Plot points with coordinates (2, 3), (3, 4), and (4, 5) on the given gr

Forward Loop Transfer Function

Consider the forward-loop transfer function in the sampled-data system as: (a) Determine the corresponding z -transform G(z) and the characteristic equation for this system. (b) Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s. (c) C

Graphs : Coloring Maps

Let G be a cubic plane graph. Prove that the map M(G) is 3-colourable iff each country has an even number of sides. note: if we omit the vertices and edges of a plane graph G from the plane, the remainder falls into connected components, called "faces." Clearly each plane graph has exactly one unbounded face. The boundary

Intepreting Data and Piecewise Functions

A factory begins emitting particulate matter into the atmosphere at 8 am each workday, with the emissions continuing until 4 pm. The level of pollutants, P(t), measured by a monitoring station 1/2 mile away is approximated as follows, where t represents the number of hours since 8 am: p(t)= 75t + 100 if 0 is less tha

Graphs : Chromatic Number

Show that the chromatic number of G_1 + G_2 isX(G_1) + X(G_2) for any two graphs G_1 and G_2. Where X(G)is the Chromatic Number. defn: X(G) a proper colouring or simply a colouring of the vertices of G is an assignment of colours to the vertices in such a way that adjacent vertices have distinct colours; X(G) is then the mi

Describing Curves and Graphs

Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. a. Y = 3X2 b. (X-1)2 + (Y-8)2 = 16 c. (X+2)2 + (Y-4)2 = 36 d. Y = X2 - X