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# Graphs and Functions

### The importance of determining the vertex of a function.

What is an actual example of when it would be important to determine the vertex of a function?

### Trees and Graphs: Does the Graph Exist?

Graphs and trees Section 11.5, #16 Either draw a graph with the given specifications or explain why no such graph exists. #16: tree, twelve vertices, fifteen edges Section 11.5, #18 Either draw a graph with the given specifications or explain why no such graph exists. #18: tree, five vertices, total degree

### Understanding the various types of graphs to represent data

What types of information can you gather from graphing a formula? (Every day use, like budgets, Surveys, etc.)

### Vector Cartesian Parametric Equations

You are given the vectors X = (1,1,1), y = (2,1,1) and z = (6,2,2). (i) Find the Cartesian equation of the plane &#928; normal to the vector x containing the point (2,1,1). (ii) Find the parametric equation of the line l through the points (2,1,1) and (6,2,2). (iii) If l' is given parametrically by l' = x + ty (with x

### Functions:Finding a residue.

Find the residue of F(z)=cot(z)coth(z)/z^3 at z=0

### Analyzing a Polynomial Function

Please see the attached file for the fully formatted problems. Find a polynomial function for the attached graph and find the solutions to the following parts. A. How many zeros does the function have? What are their multiplicities? B. Construct a polynomial function whose zeros are those identified in Part A. What role d

### Change in variables with direct and inverse proportions.

X varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and t are doubled?

### Function: Find how many x-intercepts and the location of its vertex

Without drawing the graph of the given equation, determine: (a) how many x-intercepts the parabola has (b) whether its vertex lies above or below the x- axis. SOLVE PROBLEM: y = x(to the second power) - 5x + 6

### Linear Programming

The Dub-Dub and Dub Company produces and markets three lines of WEB page designs: A, B, and C; A is a standard WEB page design and B and C are professional WEB page designs. The manufacturing process for the WEB page designs is such that two development operations are required - all WEB page designs pass through both operations

### Finding the Equation of a tangent to a circle.

You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.

### Use quadratic functions for modelling motion

A new set of automatic sliding doors at the entrance to a supermarket is being designed. The doors will consist of a pair of 100cm wide glass panels which are programmed to slide open in opposite directions when a sensor is triggered. The panels are identical except for the direction in which they move. For the purposes of this

### Functions: Change in x versus change in y

Given is the following function: k(x)=2x^2*(&#8494;^(40-x)) Is the change of the above function from delta x 42 to 42.1 approximately smaller than the delta k of 40?

### Functions and change

Given is the following function: k(x)=2x^2*(&#8494;^(40-x)) Is the change of the above function from delta x 42 to 42.1 approximately smaller than the delta k of 40? Please give full explanation of answer (mathematical evidence).

### Algebraic linear models from given data or written descriptions

(i) Copy and complete Table 1 in order to shown how the total charges under package 1 and under the two scenarios for package 2 compare for different amounts of internet access time per month (0, 1 hour and 10 hours) Table 1 ------------------------------------------------- Access per month/ minutes 0

### Find the domain and range of the functions

State the domain and range for each of the following functions (a) f(x) = ln(1 + x squared) (b) f(x) = 1 / (over) x-1 + 1 / (over) x-2

### What is sin(x/4) of my graph?

I am having problems interpreting what sin(x/4) is . I have done a graph for sin(X) and sin(x/4) from 0 to 12pi on the x axis,and this makes the x axis go to about 37.699111 radians. The sin(x) goes from 0 up to +1 on the y axis, this is about 90 degrees. Then it goes back through the x axis at about 3, then down to y-1, this is

### True and False about Characteristics of a Parabola

These questions are about the quadratic function which takes the form: y=ax^2+bx+c Where a is non-zero. Choose the false statements. A. If c=0, then the graph of y will go through the origin B. If B=0, then the graph of y will not be a parabola. C. The graph of y will have a minimum value if a is positive.

### Correlation and Regression..

Consumer Debt: Bank credit card debt has risen steadily over the years. The table gives debt per household in 1994 dollars. Year (x)      1975       1980     1985     1990     1995 Debt (y)      270       650    1100    1800    3100 a.  Plot the data.  Does the gr

### Determining the values to make a function undefined.

For what values or range of values are the following functions undefined a) f(x) = 1/x b) g(x) = Square root of (x+2)(x-3) <br>c) h(x) = 5 / x^2-4x-45

### Pivot points within a 7 point hinge

Please see the attached file for the fully formatted problem(s). My problem is explained more in my attachment, but briefly, I require some form of equation or graph to calculate where the pivot points within a seven point hinge system need to be in order for the rotating edge to rotate around a origin. The question is in

### Learning how to rearrange and graph equations.

How do I rearrange equations and then graph them?

### Graphing Regions: Constraints and Corners

Sketch the region bound by the constraints and identify the corners. 2x + 3y is < or = 6 5x + 2y is < or = 10 x is > or = 0 y is > or = 0

### A Real-life Application of Rational Functions

Describe the cost C(x), in millions of dollars to inoculate x % of the Canadian population against a particularly virulent strain of flu C(x)=130x ____ 100-x a) sketch the rational function showing only the regions of the curve that are relevant in the context of this problem (ie. an appropriate domain) b) e

### Maximizing a function: Example problem

The graph below shows the constraints of the objective function: P = 3x + 2y The shaded area is the set of all feasible points. Using the graph above, find the maximum value of the objective function.

### Saturating functions

I am doing a report on saturating functions and i need to know everything that there is to know about them.

### Calculating the distance from one point to another.

What number is 3/5 of the way from -4/7 to 1 1/8?

### Finding the vertex and intercepts - repel or attract

Rewrite the function f(x)=x^2+13/3 x+7/3 in the form f(x)=(x+13/6)^2+ c Then need to find the vertex of parabola as the graph of f, finding the y and x intercepts. Find the fixed points of f state whether they repel, attract or are indifferent. Using a gradient, find the interval of attraction for one of the fixed

### Finding vertex and intercepts for an equation

Find the vertex and intercepts for the Quadratic function, and sketch its GRAPH in WORD. Show all steps to solving the problem. Y = -x^2 + 2x + 3

### Finding vertex and intercepts for an equation and sketch a graph using Word

Find the vertex and intercepts for the Quadratic function, and sketch its graph using word. y = x^2 + 2x - 24

### Calculating the y intercept given data points and the slope.

What is the y intercept for p(3,5)q(4,6), m=2?