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# Graphs and Functions

### Finding the vertex and intercepts of a parabola.

Find the vertex and intercepts for each parabola. Graph using Microsoft Excel. g(x) = x^2 + x - 6

### For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time.

Using the formula A=P(1 + r/n)^(nt), let r=8%, P=1, and n=1, and give the coordinates (t,A) for the points where t=0, 1, 2, 3, 4. Round your answer to the 100th place. How do you graph this? I am confused.

### Finding Areas Bounded by Functions

Please see the attached file for the fully formatted problems. keywords : find, finding, calculating, calculate, determine, determining, verify, verifying, evaluate, evaluating, calculate, calculating, prove, proving keywords: integration, integrates, integrals, integrating, double, triple, multiple

### Step Functions and Absolute Value Functions : Determine where the function is continuous.

Determine where the function f(x)= x + [|x^2|] - [|x|] is continuous. I think the correct answer is that the function is continuous for its domain but not defined at x=0. Can someone explain this problem to me and help me understand the greatest integer and absolute value functions? keywords: continuity

### Algebra Questions

(See attached file for full problem description) 1) An open-top box is to be constructed from a 4 foot by 6 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

### Slope Predictor Formula : Finding a Tangent Line to a Curve

1. Apply the slope-predictor formula to find the slope of the line tangent to y = f(x) = (2x+4)2 - (2x-4)2. Then write the equation of the line tangent to the graph of f at the point (3, f(3)). My attempt... I found y first by: f(x) = (2x+4)2 - (2x-4)2 f(x) = (4x2+16x+16) - (4x2-16x+16) f(x) = (4x2+16x+16) + (-4x2+

### Square root equations

Solve the following equations and show your work: 1) sqrt of x - 2 = 1 2) sqrt of x^3 = 27 3) 3 sqrt of x^2 = 9 4) Is (sqrt of x)^2 an identity (true for all nonnegative values of x)? x -2 -1 0 1 2 y .111 .333 1 3 9 Given the table above, graph the function, identify the graph of the function (line, parabol

### Graphing a Function using a Table of Values

For the function, y= 1 ---- x-2 a) Give the y values for x = -2, -1, 0, 1, 2, 3. b) Using these points, draw a curve. Show graph here. Please explain how to plot the graph, once I find the y values, x is already given. Please explain and show in detail how t

### Solving Linear Equations Word Problems

Section 3.1 # 94 Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is \$5.00 per can. After experimenting with the prices for some time. Helen has determined that the weekly demand can be found by using the equation D=600-40p, Where d is the number of cans and p is the

### Solving and Graphing Linear Equations and Word Problems

Week 3 Discussion Questions-Linear Equations in 2 Variables 1. Paul and nine other students are taking a math class. He is worried about the content of the next quiz because he just can't solve those word problems. The teacher has said that the number of questions divided by the number of students = 2.8, and 14.3 % of the tes

### Radicals : MTH133 Unit 3

1) 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 nonnegative values of x)? Answer: Explain your answer in this space. 3) x -2 -1 0 1 2 y .111

### Y=x^2-6x+8 in to the form y=a(x-h)^2+k

Y=x^2-6x+8 in to the form y=a(x-h)^2+k How do you change the function? This initial problem is followed by: a) What is the equation for the line of symmetry for the graph of the function. (I think I can solve this ) Please explain and show in detail how to break this down in (dummy language) b) Asks that the functi

### Find a value for C so that f(x) is continuous for all of x.

Find a value for C so that f(x) is continuous for all of x. See attached file for full problem description.

### IP unit 1: Algebra Questions - Graphing, Domain, Range, Slope

1) a) Given the above 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. Graph Type: Explantation: Domain: Range: b) Given the above graph, identify the gr

### Graphing Word Problems

In most businesses, increasing prices of products can negatively impact the number of customers. 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 e

### Graphing Problems for Functions

1. (a) - (c) 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. 1. (d) Given a line containing the points (1,4), (2,7), and (3,10) determine the slope-in

### Fixed Point Iterations

1. The equation x - 3 ln x = 2 has exactly two solutions A and B, with 0 < A < B. (You do not have to show this.) (a) Show that A is in [0.5,0.7], and B is in [8.3,8.5]. (b) Consider the following fixed-point iteration for finding a solution of the given equation: xn+1 = e(1/3(Xn-2)): Show that if X0 = B+ E, where E is

### Using a Graph to find the Maximum Area Enclosed; Volume Calculations

A rancher is building a rectangular corral and is using one wall of his barn as one of the sides. Because the barn wall is quite long, he needs fencing only along the other three He has 500 feet of fencing. The rancher wants the area of the conal to be as large as possible. should he choose as the dimensions of the corral? (Don'

### Identify and graph a conic

Identify and graph the conic. Then rewrite it in Cartesian coordinates. r = 3/[4+sin(theta)]

### Increasing function on open interval

Prove that if f is an increasing real-valued function on an open interval (a, b), then, for all but at most countably many points c in (a, b), Lim_(x-->c) f(x) exists and is equal to f(c).

### Continuous Functions : Strictly Positive and Strictly Increasing

x Prove that if f is continuous and strictly positive on [a,b] and F(x)=&#8747;f then F is strictly increasing on [a,b]. a

### Word Problem: graphing and solving equation

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 an

### Vertex, Focus and Directrix of Parabola and Ellipse

1. Find the equation of a parabola whose vertex is (0,0) and directrix is the line y=3. 2. Find the vertex, focus, and directrix of (x-2)^2=12(y+1). Find the latus rectum and graph the parabola, making sure that all points and axis are labeled. 3. Find the equation of the ellipse whose center is the origin and has a

### Selected amounts at December 31, 2003 from the Hay and Barnabas Company's information system appear as follows:

Selected amounts at December 31, 2003 from the Hay and Barnabas Company's information system appear as follows: Cash paid employees for salaries and wages 300,000 Cash collected from sales customers 1,850,000 Bonds payable 500,000 Cash 150,000 Common stock 60,000 Eq

### Mappings, Injective and Surjective Functions and Cycles

1. Let f : X -> Y and g : Y -> Z be mappings. (1) Show that if f and g are both injective, then so is g o f : X -> Z (2) Show that if f and g are both surjective, then so is g o f : X -> Z. 2. Let alpha = 1 2 3 4 5 and Beta = 1 2 3 4 5 3 5 1 2 4 3 2 4 5 1 .

### How do you use linear equation in business?

In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges \$2.00 for a ride. They conducted a survey of their customers and found that they will lose approxima

### Petersen Graph Nonplanar

Show that the Petersen graph is nonplanar by a) showing that it has k3,3 as a subcontraction, and b) using the problem 1 show above part a) You don't have to solve problem 1. Can you explain about contraction. problem 1.-Let k>=3 be an integer , and let G be a plane graph of order n(>=k) and size m. a) If the length

### Bipartite Graphs

A) Show that every bipartite graph G is a subgraph of a -regular bipartite graph. b) Show that every bipartite graph G is of class one , that is, What does -regular bipartite graph mean? Can you draw a graph for me please?

### Show that every nonempty regular graph of odd order is of class two.

Show that every nonempty regular graph of odd order is of class two. Please explain with details. Draw a graph.

### Trees and Graphs : Outerplanar Graphs

What bound is given for X(G) by the theorem "for every graph G, X(G)<=1+max &(G') ,where the maximum is taken over all induced subgraphs G' of G" in the case that G is a) a tree? b) an outerplanar graph. Note: -&(G') this sign represent the minimum degree of G'. Yes it is that minimum -A graph G is outerplana