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# Graphs and Functions

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: 1. Search the Internet and the Cybrary to find the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002.: o heart dis

### Function solutions

2. Given the polynomial f(x) = 2x 3 -5x2-4x+3, find the solutions if the function is completed as a) f(x) =0 b) f(x+2)=0 d) f(2x) = 0

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

I need the following info: Find the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002. Heart disease Cancer AIDS Plot The data for each disease as points in a rectangular coordinate system. Using a smooth line, connect your dat

### Prove A Variation of Fermat's Theorem

There always exists a real number n such that a^n = b^n + c^n , where a, b and c are any integers. The problem is not Fermat's Last Theorem, but a variation of it with real exponents.

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

I am presenting this information as a speaker to present statistical information at a conference. To prepare, this information is important: Finding the number of deaths in the United States due to each of the following medical conditions in each of these years; 1985, 1990, 1995, and 2002.: Heart disease Cancer AID

### Functions: Onto and One-to-one, Bijections and Functions

Please help with the following problems on graphs and functions. Provide step by step calculations. 1. Assuming A,B not equal to no solution, define m1:AxB->A and m2:AxB-> as follows: m1(x,y)=x and m2(x,y)=y. If f: A->B, show that a) f onto=>m2 |f is onto b)f one-to-one=>m2 f is one-to-one 2. Assuming f: A->B and g:

### Given a graph of a trigonometric function find period, amplitude, phase shift and equation.

The figure below shows the graph of a sine function - y is a function of &#952;, with &#952; measured in degrees. For this function state: a. its Period b. its Amplitude c. its Phase Shift from the sine function y = sin2x d. the Equation of the Function Answer in degrees also please Please see attached.

### Functions and Graphs: Trends and Real World Implications

Plot your data for each disease as points in a rectangular coordinate system. Year...................1985..........1990..........1995......2002 Heart Disease 771,169 720,058 684,462 162,672 Cancer 461,563 505,322 554,643 557,271 AIDS * 8,000 25,188 39,979 14,095 - Use individu

### Statistics

What is the "causal relationship" between independent and dependent variable?

See attached

### Find the equation of a line given two points.

Find the slope-intercept form of the linear equations that go through the following points: (-1,6) and (1,2) also through points (5,3) and (-2,3).

### Finding the Maximum Height by Graphing

If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then its height is a function of time, given by s(t) = -16t squared + 64t. How would I graph this function for 0 ≤ t ≤ 4? And how do I determine the maximum height reached by the ball?

### Quadratic Equation Application: Area, Maximum Values & Intercept

1. Given the quadratic equation y=-x2 + 8x + 9 a. Find the x and y coordinates of the vertex b. What is the y-intercept? c. What are the x-intercepts? d. If you graph the parabola, would it open up or down? 2. You have enough grass seed to cover an area of 300 square feet. You want to install fencing around the a

### Systems of Equations : Solve by Graphing and Addition

Solve each system by graphing: 1) y=2x y=-x+3 2) y=2x-1 2y=x-2 3) 3y-3x=9 x-y=1 4) y=x-5 2x - 5y=1 5) y=x+4 3y-5x=6 6) x-y=5 3y-5x= 6 7) x-y =5 2x=2y=14 8) 2x-y=4 2x=4x-6 Solve each system by addition method. 9) x+y=7 x-y=9 10) x-y=12

### Function Classification

Can the graphs (attached) be classified as functions? Explain. (A graph, using smooth lines that connect data in the graph)

### Functions and Graphs : Heart Disease, Cancer and AIDS - Trends and Real World Implications

1985 1990 1995 2000 Heart Disease 778375 727206 737,563 710760 Cancer 459121 510426 538,455 1220100 AIDS 1700 25370 43115 14999 I do not understand how to plot data. I need to do this f

### Real-Life Applications of Functions Versus Relations and Reversal of Variables

In the real world, what might be a situation where it is preferable for the data to form a relation but not a function? If the variables in an equation were reversed, what would happen to the graph of the equation? For example, how would the graph of y = x² relate to the graph of x = y²?

### Sketching the graph of a swimming fish's energy

Any help is greatly appreciated; I found this problem pretty frustrating. I replaced the "less than" symbol with the words "less than" because the computer seemed to have a hard time recognizing the symbol. "For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3.

### Completeness

7.4.2 Show that the following family is not complete by finding at least one nonzero function u(x) such that E[u(X)]=0, for all theta >0. f(x; theta)= 1/(2*theta), -theta <x< theta where 0<theta<infinity and 0 elsewhere. The answer is Xbar.

### Functions : Maximizing Profit, Diminishing Returns and Maximizing Volume

1. The demand for a product in dollars is given by p(x) = 53/(x)^1/2 Fixed cost are \$608 and the cost to produce each item is \$0.53. Find the production level of x that maximizes profit within the range of 0<(or equal to)x< (or equal to)7530. 2. An efficiency study of the afternoon shift (12:00-4p.m.) at a factory shows th

### Intercepts, Vertex, Line of Symmetry and Image Set

This question concerns the parabola which is the graph of the function: f(x) = [1/4(x-2)^2] -1 a) Explain how the graph of the parabola can be obtained from the graph of y =x[squared] by using appropriate translation and scalings. b) Using your answer to part (a), or otherwise, write down the coordinates of the vertex of th

### Trigonometric Functions : Explain sine, cosine, tangent, cotangent functions and inverses.

Please explain sine, cosine, tangent, cotangent functions and inverse trigonometeric functions like arcsin, arccos, arctan and arccot functions with graphics.

### Polynomial functions, inverses, half-life, investments

Please find the attached. 1) Fit a polynomial Function f(x) to the graph. The scale on the x-axis is 1 and the scale on the y-axis is 5. The point (1,12) is on the graph, Assume that if the graph appears to cross the x-axis at a mark, it really does. (1,12) 3 2 1 4 2) Noise level in decib

### Fixed Point : Mean Value Theorem

A number (a) is called a fixed point of a function (f) if f(a)=a. Prove that, if f'(x) does NOT equal 1 for all real numbers (x), then f has at most one fixed point.

### Parallel Lines

Find the pair of parallel lines: 1: -y=-x+2 2: -2y-2x=2 3:-2x+2y=2 Not sure how to do the above problem.

### Minimum Value of Closed, Continuous Analytic Function

5. Use the function f(z) = z to show that in Exercise 4 the condition f(z) does not equal 0 anywhere in P is necessary in order to obtain the result of that exercise. That is, show that |f(z)| can reach its minimum value at an interior point when that minimum value is zero. Please see the attached file for Exercise 4 and the

### Equations of Lines, Slopes, Intercepts and Word Problems

Please see the attached file for the fully formatted problems. 1. Find a linear function perpendicular to the function y= -5x + 12 at the point (2,5) in standard form, point slope form, and slope-intercept form. The orginal line is y = -5x + 12 (slope is -5), so the perpindicular line will be y = 1/5x + ? 5 = (1/5)2 + ?.

### Analytic Functions : Constancy

7. Let a function f (z) be a analytic in a domain D. Prove that f (z) must be constant throughout D if (a) f (z) is real-valued for all z in D (b) | f (z) | is constant throughout D. (Question also included in attachment)

### Graphing the Rational Function

Please graph the following rational function and show all of the necessary work involved: x^2 + x - 2/ 2x^2 + 1

### How to Graph the Rational Function

Consider the following rational function: x^2-4/ x - 1 Now graph this function.