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Graphs and Functions

Find the interval on which the function

See attached file for full problem description. Find the interval on which the function 2 2 ( ) ( 2) ( 3) f x x x = − + is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.

Problem set

Question 1 Consider the functions f(x) = x^2 and g(x) = square root of x, both with domain and co-domain R+, the set of positive real numbers. Are f and g inverse functions? Give a brief reason. Question 2 Given the Hamming distance function f: A X A -> Z defined on pairs of 8-bit strings, (where A is the set o

Measurable Functions

Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x. Please make sure to show the proof in both directions.

Value of function at a given point

1. The number of 4-year college, public and private, in the period 1980-1996 can be modeled by f(x)=0.0003x^3 - 0.007x^2+0.058x+1.957 0 less than or equal to X less then or equal to 16 Where X is the number of years since 1980 and f(x) is the number of 4-year colleges measured in thousands. Determine the average number

graph the functions with data points

For the function, y = ___1____ x - 2 a) Give the y values for x = -2, -1, 0, 1, 2, 3. Answer: Show work in this space. b) Using these points, draw a curve. Show graph here.

Graphs and Solving Linear Equations Word Problems (20 Problems)

Solve the following equations for the unknown. 1. 5x = 20 2. 7x - 3 = 18 Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph. 3. y = x + 3 4. y = -2x - 7 5. 2x + 3y = 9 6. A consumer electronics c

Break even analysis: Labor intensive firm and capital intensive firms

Draw two break-even graphs-one for a conservative firm using labor-intensive production and another for a capital-intensive firm. Assuming these companies compete within the same industry and have identical sales, explain the impact of changes in sales volume on both firms' profits. Although no example is provided in the

Equations of Straight Lines

1. Graph line with equation y=-4x-2. 2. 2x=8y=17=0 3. Graph the line with slope -2 passing through the point (-3,4). 4. Find slope of the line graphed (-44, 28) (9, -12). 5. x=9 graph the line 6. 6x-9y+7=0. 7. 2x=5y+3 8. Write an equation of line (0, -4). 9. A line passes through the point (6, -6

Asymptotes, Descartes's Rule and coordinates of the vertex

1. f(x) = x^3 + x^2 - 4x - 4. (a) What is the end behavior of this function? (Does it go up or down to the left? Does it go up or down the right?) (b) What is the maximum number of turning points for this function? 2. Give the coordinates of the vertex of the parabola y = (x + 2)^2 + 5. 3. Use Descartes's Rule of Sig

Simplifying and Solving Equations with Exponents

1. Simplify the expression using properties of exponents. Answer should contain positive exponents only. (3x^2y^3)^2(3xy)^2 / (2x^4y^3)^-3 2. Solve for X: 3/x - 1/x+2 = -2/3x+6 3. Use the quadratic formula to solve for x: x^2 -4x + 2 = 0 4. Solve for x by factoring: x^3 + x^2 - 6x =

Euler Function

(See attached file for full problem description) Conjecture: Suppose that m and n are positive integers. If gcd(m,n)=1, then . a. If m and n are positive integers and k is any integer, show that gcd(k,mn)=1 if and only if gcd(k,m)=1 and gcd(k,n)=1. b. Suppose gcd(m,n)=1. Prove that establishes a bijection between

Exponential Growth and Decay Projects

Think of one real situation that involves exponential growth and that involves exponential decay. for each example, your project should include the following: * Paragraph - Briefly explain the situation. You may make up your own information, but make it realistic. Include the facts needed to write an equation. * Equation -

Real-Life Applications of Hyperbolas and Parabolas

One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing

One-to-One and Onto Functions

Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X → Y is one-to-one and the function g : X →Y is onto. (i) Use the function f to show that m ≤ n. (ii) Use the function g to show that m ≥ n. (iii) Is f : X → Y onto? Justify your assertion. (iv) Is th

Input-output Tables and Equations of Lines, Slope and Intercept

Decide whether the relation is a function. 1- (6,5), (4,3), (-2,3), (0,-1) , (-1,2), (-4,-5), (-3,4) 2- (4,4), (3,3), (-1,1), (6,6), (1,-2) make an input-output table for the function rule. Use a domain of -10,-5,0,5, and 10. Identify the range. y=8x+1 y=-6x y=x square 2+5 write a function that relates and x and

Domain values

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

Examples of Arithmetic series and sequence

Details: Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadrat

Volume function

The volume of a cylinder (think about the volume of a can) is given by V = πr2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function of r.

Algebra Description Graphed

Please answer the following questions ASAP: Match each description of a graph with an equation. The graphs are all described in relation to the graph y = x^2 shifted 3 units upward shifted 3 units to the left shifted 3 units downward stretched out and flipped upside down shifted 3 units to the right

Quadratic function

Given the quadratic function (see attached file) a.) Does the graph open up or down? b.) What is the equation of the axis of symmetry? c.) What are the coordinates of the vertex? d.) Give the y intercept e.) Give the x intercept(s) f.) sketch the graph

Math problems help

1. Find an equation of variation where y varies jointly, directly as the cube of x and cube root of z, and inversely as the square of w, and y = 4 when x = 2 and z = 8 and w = 4. 2. Perform the indicated operation and simplify. y2 + 3y y2 -y y - 1 y2 -5y + 6 (y-3)(y+2)

Rational function

For the rational function (see attached), give the intercepts and asymptotes and sketch the graph.