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Graphs and Functions

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.

Applications of Graphing and Word Problems

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: Explanation: Domain: Range: b) Given the above graph,

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

Three problems involving solution to functions using the graphing method.

1. Approximate real zeros with zoom and trace (on calculator) for the given function. 2. Sketch graph of 2 rational functions as sketching aids, check for intercepts, symmetry, vertical asymptotes, and horizontal asymptotes 3. The management at a factory has found that the maximum number of units a worker can produce in a

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

Slope and Intercept

1. Simplify: (3x^-2y^3)^2(3xy)^-2 / (2x^4y^3)^-3 2. Solve for X: 5 + sqrt3x + 1 = 9 3. State the slope and y-intercept of the line given and graph on the axis: 3x - 4y = 12

Problem Set

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 -


(See attached file for full problem description)


(See attached file for full problem description) Prove: The function f from the metric space X into the metric space Y is continuous if and only if is closed in X whenever F is closed in Y.

Euler Function

(See attached file for full problem description) --- We consider the special case when m=3 and n=4. (a) Write down the correspondence between numbers in and pairs of integers in given by the function f. In other words, write out the 12 values f(a) where . (b) Fore each value you computed above, circle the equations

Perfect Numbers

An integer n is called k-perfect if σ(n) = kn (note that a perfect number is 2-perfect). (a) Show that 120 = 23? ? ? 3 ? ? ? 5 is 3-perfect. (b) Show that if n is 3-perfect and gcd(3, n) = 1, then 3n is 4-perfect.

Congruences of Modulos

Show that if and , then . (This shows that the function g is well-defined from to ) Note: g is defined as follows: g: Where is the multiplicative inverse of m1 modulo m2 and conversely. Please see the attached file for the fully formatted problems.

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 as

Functions : 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

Matlab standard deviation ( std ) function

Given a 2 x 2 matrix sample = 2.0000 + 3.0000i 1.0000 + 2.0000i 4.0000 + 5.0000i 2.0000 + 1.0000i >> std(sample(:)) ans = 2.1213 >> According to matlab the answer is 2.1213. I'm not arriving at that answer. I need to see all work on how to achieve said result.

Proving that f is not uniformly continuous

The following theorem could be used to write the proof. A theorem states that if d:D-->R is uniformly continuous on D iff the following condition is satisfied: If un and vn are both sequences in D, then lim as n-->infinity (f(un)-f(vn))=0 Show f is not uniformly continuous on D making use of the sequent

Equation of a conic section

Identify the type of graph that each equation has without actually graphing. x=3y^2 + 5y - 6 Equations may need to be simplified first.

Slope of a roof

A roof rises 7.25 ft over a horizontal distance of 13.71 ft. What is the slope of the roof to the nearest hundredth? A) 1.89 B) 0.53 C) 1.87 D) 0.77