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# Graphs and Functions

### Graphing Compound Interest

I know that 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)^m, let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. Can you show me how you got the coordinates and how to graph

### Value of x using a graph

An open-top box is to be constructed from a 6 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. When this is graphed for the function V that represents the volume of x, on the graph what is the function of

### Find the function for volume of an open-top box.

If I have an open-top box that is to be constructed from a 6 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. How do I find the function V that represents the volume of the box in terms of x? How do you

### Statistical Information

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks: The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002.

### Graphing functions

How do I graph the functions y=x and y=the sq root of x on the same graph (by plotting points if necessary). How would I show the points of intersection of these two graphs? How would the graph relate to solving all the values of x for the equation x-the sq root of x=0?

### Algebra Functions and Graphs

It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002. Year Disease 1985 1990 1995 2002 Heart Disease 771169 720058 737563 696,947 Cancer 461563 505322 538445 557,271 Plot this data

### Similar parabolic graphs

How do these graphs compare? y=x^2 & y = x2 - 4x - 5

### Functions

Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2). v0 is the initial veloci

### Function

For the function y = x2 - 4x - 5 How do I put the functionin the from of y = x2 - 4x - 5? and what would the line of symmetry be?

### Expressing a Word Problem as an Equation

If it is 300 miles from Chicago to St. Louis in a car traveling a constant speed of 60 mph, how do I write a linear function that expresses the distance to be traveled to reach St. Louis, s, as a function of time, t?

### Value of Y in a function

For the function y= 1/x-1 Give the y values for x=-2,-1,0,1,2,3?

### Riemann Zeta Function

Is is shown that the Riemann Zeta function for positive even integer k which is the sum from 1 to infinity of 1 / n^k = 2^(k-1) abs(B_k) pi^k / k! See attached for clarification.

### Revenue and Cost Functions and Break-Even Point

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break even point is: A. (17, 374) B. (242, 9) C. (11, 242) D. (31.5, 661.5)

### Find the equation of a line given two points : (8,6) and (2,-4)

Problem: The equation of the line through (8,6) and (2,-4) is A. 5x-3y = 22 B. y=3/5x = 8/5 C. 3x=4y = 48 D. -4x = 2y = -16

### Function : f(x) = (x+2)(2x-3). f(-2) =

Problem: f(x) = (x+2)(2x-3). f(-2) = A. 0 B. 4 C. -6 D. -14

### What are the critical points of f(x, y) = y^2 + x^3 + 3x^2?

Find and classify the critical points of: f(x, y) = y^2 + x^3 + 3x^2.

### Equation of a line given two points : Write the equation of the line passing through the following points: f(9) =2 and f(7) = 5.

26. Write the equation of the line passing through the following points: f(9) =2 and f(7) = 5.

### Functions and Difference Quotients

Use f(x) = -2x^2 + 3X 21. Find f(-4) 22. Find f(9x-1) 23. Find the difference quotient

### Prove Composition of Functions are Associative

Prove, from the definition of function (using ordered pairs), that composition of functions is associative. (i.e. prove that f * (g*h) = (f* g) *h) for suitable functions f, g, h I would like to know how to use ordered pairs to proof the associative of composited functions.

### Differentiability, Bounded Above and Supremums

1. Let A and B be two nonempty sets of real numbers. Define A+B = {a+b: a belongs to A and b belongs to B}. (a) Show that if A is open, then A+B is open. (b) If A and B are both closed, is A+B closed? Justify your answer. 2. Let f be differentiable for x > a and A as x --> infinity. Prove that there is a sequence x_n --> infi

### Graph and simultaneous equations

Accurately and neatly graph and label each of the equations and estimate the point of intersection of the two lines. Mathematically solve for the exact point of intersection of your two lines compare your mathematical solution with your graphical solution. Similar? Why? Not similar? Why or why not x + 2y = 14 4x - 2y = 18

### Properties of additive functions; Bounded; Continuous; Measurable

Let f : R --> R be an additive function i.e. f(x+y) = f(x) + f(y) for all x,y in R. 1. If f is bounded at a point, then f is continuous at that point. 2. If f is measurable, then f is linear i.e. f(x) = cx for some c in R. I have already proved that f is continuous if and only if f is linear, and I have proven that if f i

### Length of Polygonal Line Segments and Length of a Curve and Distance Formula

Find the total length of the polygonal line segments joining the points (xi, f(xi),i=0, 1,...,n, zwhere a= x0,x1,... xn=b is a regular partition of (a,b). use the indicated values for n (1) f(x) = sqrt x, a=0,b=4 (a) n=2, (b) n=4 (2) f(x) = sin^2 x, a=0, b= 2pi (a) n=2 (b) n=4 (c) n=8 (3) Use a y integration to find

### Solve the following linear program using the graphical solution

(See attached file for full problem description with proper equations and diagrams) --- Graphical solution procedure Please help solve this linear problem in the attachment using the graphical solution procedure & graph the feasible region: Solve the following linear program using the graphical solution procedure: M

### Directed Graphs, Vertices and Distinct Paths

6. Recall that R^3={(x,y,z):x,y,z(subset of R)}. Let G(V,E) be a directed graph, in which V= {(x,y,z)-(subset of R^3) :x,y,z(subset of R),-10<=x,y,z<=10}. Suppose that for any vertex, v=(x,y,z)--[subset of V], the only edges originating at v are the ones joining v to (x+1,y,z),(x,y+1,z),(x,y,z+1) . i.e. any path that originate

### What are all the intercepts of the graph of...? (6 Problems)

20. At what points does the graph of y = x^2 - 3x -10 cross the x-axis 21. What are all of the intercepts of the graph of y = 15x^2 + 89x - 6? 22. What are all the intercepts of the graph of y = 2x^2 - 11x + 5? 23. What are all the intercepts of the graph of y = 6x^2 + 13x + 6? 24. What are all the

### Maximum Modulus Theorem Problem

Let f be analytic in the disk B(0;R) and for 0 =< r < R define A(r) = max { Re f(z) : |z| = r}. Show that unless f is a constant, A(r) is a strictly increasing function of r. Please justify every step and claim and show how you used all what is given. Also refer to theorems or lemmas used in the proof. The section where I

### Equal Terms Compared

Provided a and b are not zero, how does a/b compare to b/a? In other words, if a/b=c , then what does b/a equal in terms of c?

### Problem Set

Solve this inequality state the solution set using interval notation and graph the solution # 26. 3 2 ---- > ------- x + 2 x - 1 Page 576 Find the vertex and intercepts for each quadratic function and sketch its graph. # 49. y = x^2 - 4x - 12 # 50. y = x^2 + 2x - 24

### Functions : Let f(x) = 4x-9. Find all x for which f(x) =2

Let f(x) = 4x-9. Find all x for which f(x) =2.