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Graphs and Functions

Left-Side and Right-Side Continuous Functions

We define the floor function [[x]] to be the greatest integer not exceeding x. For example[[4]]=4 [[2.37]]=2 [[-1]]=1[[-1.2]]-2 Sketch by hand the graph y=[[x]] by first tabulating the values pf [[1]] for several numbers x. Then compare your graph with the plot from a graphing calculator. What are the discontinuities of f(x

Randomly Eulerian Graphs

Let G be a graph that is randomly eulerian from a vertex v. Show that if deg u = Delta(G)"max degree in G", then G is randomly eulerian from u.

Forests and Eulerian Graphs

Let F be a forest. Add a vertex x to F and join x to each vertex of odd degree in F. Prove that the graph obtained in this way is randomly Eulerian from x, and every graph randomly Eulerian from x can be obtained in this way.

Randomly Eulerian Graphs

Recall that a graph G is randomly Eulerian from a vertex x if and maximal trail starting at x in an Euler circuit. (If T = xx_1 ... x_l, then T is a maximal trail starting at x iff x_l is an isolated vertex in G - E(T).) Prove that a nonempty graph G is randomly Eulerian from x iff G has an Euler circuit and x is contained in ev

Eulerian Graphs

Give examples of eulerian grpahs that are randomly eulerian from exactly none, one, two or all of their vertices.

Eulerian Graph

Let G be an eulerian graph of order n >= 3. Prove that G is randomly eulerian from exactly none, one, two or all of its vertices.

Area of ellipse and slopes of f & f(inverse)

1) find the area of the enclosed region between the curve and the coordinate axes x^2/8 + y^2/6 =9 the graph is just the coordinate system with an ellipse draw over it, no numbers or letter are present 2) if f(x) =x^2 (x>=0) and f(inverse) = x^1/2, show that the slopes of the graphs of f(x) and f(inverse) are recipr

Vertex of a Parabola

I need to understand how to find the vertex of a parabola two ways. Show examples

Graphing Second-Order and Third-Order Rational Functions

I do not understand how to conduct these equations I Excel so that I can show a graph of each. Choose a second-order/third-order (e.g., x2/x3) and a third-order/second-order (e.g., x3/x2) rational function. Provide a graph for the second-order rational function (e.g., x2), choosing x values in the range from -10 through +10.

Graphing and Tangents

A) Graph b) Draw tangent to graph @ points where x coord. are -2, 0, and 1 c) f(x) by determining Limit h>0 f^'(x+h) - f(x) / h d) f^' (-2), f^' (0), and f^' (1) (should meet slopes in part b) f(x) = 1/2 x^2

Graphs and Linear Equations

1. The following table shows the height of a tree as it ages. In Excel, plot each point on the same graph where the first coordinate is the age of the tree and the second coordinate is the height of the tree (age, height). After plotting each point, explain if there is a linear relationship between the age and height of the tr

Graphs and Limits

Graph each function then find specified limits. Exist? f(x)=x^2 ; Find lim x--> -1 f(x) and lim x--->0 f(x)

Parallel Lines

Suppose the government mandated gasoline prices to remain constant at $4.26 per gallon everywhere across the country, restricting gas stations from increasing the price in the future. The law will take effect in 2012. Is there an equation that would illustrate the price of gas under the new law? Is there an equation that i

Question About Plotting a Function

Find the intercepts, slope, asymptotes, relative maxima and minima, and intervals of increase or decrease of the function and plot it. f(x) = x^4 + 2x^3

Find an equation of the tangent line to the graph.

Find an equation of the tangent line to the graph of the relation given by x2 - xy + y2 = 7 at the point (2, 3) . x + 4y - 14 = 0 4x + y - 11 = 0 11x + 4y - 34 = 0 7x + 3y - 23 = 0 17x + 8y - 58 = 0 none of these ∫ 3/x^2/5 dx = (15/2)x^

Equation for the tangent line to a graph.

Please choose the correct answer and indicate final answer. 11. f(x) = (x + 4)^1/2. An equation for the tangent line to the graph of f(x) at the point where x = 77 would be x - 6y + 13 = 0 x - 8y + 20 = 0 x - 10y + 29 = 0 x - 12y + 40 = 0 x - 14y + 53 = 0 x

Maximum Value of Functions

A jewelry floor safe with a square base is to be made so as to have a total volume of 648 cubic inches. The side material for the safe costs $1 per square inch. The material for the top costs $4 per square inch while the material for the bottom costs $2 per square inch. What, in inches, would be the height of the most economical

Points of Inflection

Find the x-coordinate of the points of inflection of f(x) = 47 + 13x + 18x^ 2 + 4x^ 3 - x^ 4 -3, 1 -1, 3 -3, -1 1, 3 -4, -1 1, 4 -4,1 -1, 4 none of these

Slope Predictor Formula and limits

See attached file for full problem description. 1. Apply the slope predictor formula to find the slope of the line tangent to y = f(x) = (2x + 4)^2 - (2x -4)^2. Then write the equation of the line tangent to the graph of f at the point (3, f(3)). 2. Find all points on the curve y = (x+4)(x-5) at which the tangent line is horiz

Solving Equations and Graphing

(u+23)^ 1/2 = 9 Graph 22) y =0.3x Since any real number can be used in place of x in y = 0.3x the domain is (-oo, oo) Since any real number can be used in place of y in y = 0.3x the range is (-oo, oo)