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# Graphs and Functions

### Sketch a Graph that Fits the Data

Use the given information to draw the graph of f(x) on an interval near the indicated point (x=3). If there is not enough information given, then state this fact. f(3) =2 f ' (3) = DNE f ' (x) < 0 for x < 3 f ' (x) > 0 for x > 3 f " (x) < 0 for x < 3 f " (X) < 0 for x>3

### Graphing Functions and Descartes' Rule of Signs

1. Use Descartes` Rule of Signs to determine the possible number of positive real zeros of the function. F(x)=3x cube-4x squared-2x-4 ***************x squared +11x+28 2. Graph: f (x)= ------------------------ ***************x squared +8x+16 ****************3x squared -3x-1 3. Graph: f (x)= ------------------------ ***

### Functions / Graphs : Domain, Range, Distance Between Points

1. Find the domain and range of the function: f(x)=6xsquared+4 2. Find the distance between the two plotted points;(-5,2) (4,-4) 3. Using graph of f(x)=x squared as a guide, graph the function; g(x)=(x-3)squared+4 _____________________________________________________________________ 2

### Functions and Graph: Slope, "Parallel, Perpendicular or Neither"

1. Find the slope of the line passing through the pair of points (2,-8), (2,2) Answers A.0 B.5/3 C.undefined D.5/2 2. Determine whether the graph of the equations are parallel, perpendicular, or neither -8x-7y=8 6x-2y=8 3. Find the vertex of the graph of the function; f(x)=(x+2)second power=4 A.(-2,-4)

### Graphs : Y as a Function of X

1. Which equation defines y as a function of x? answers a. y=-3x+4 b.y=-3 c.-6x second power -3y second power=4 d.x=10 2. m=-4/5,(5,7) answers a.5x=4y=-15 b.5x=4y=55 c.4x=5y=55 d.4x=5y=-15

### If r = xi + yj + zk and R denote &#9553;r&#9553;, Verify (1) &#9660;R^n = nR^(n-2) r (2) &#9660;×(R^n r) = 0 Verify (1) &#9660;*(F + G) = &#9660;*F + &#9660;*G (2) &#9660;×(F + G) = &#9660;×F + &#9660;×G

Real Analysis Gradient, Divergence and Curl (I) If r = xi + yj + zk and R denote &#9553;r&#9553; Verify (1) &#9660;R^n = nR^(n-2) r

### Conditional Mass Function

#40. Two dice are rolled. Let X and Y denote, respectively, the largest and smallest values obtained. Compute the conditional mass function of Y given X = i, i = 1, 2, 3, 4, 5, 6. Are X and Y independent? Why? (Question is also included in attachment)

### Polynomials, Equations, and Radicals: Please respond in excel format. See the attached file for complete description.

43. (3y+2) (2y^2-y+3) *44. (4y+ 3) (y^2+3y+1) 46. (m^3-4mn^2)(6m^4n^2-3m^6+m^2n^4) *90. (5-6y)(3y^2-y-7) *91. Office Space. The length of a professor's office is x feet, and the width is x+4 feet. Write a polynomial that represents the area. Find the area if x=10ft. 100. If a manufacturer charges p dollars each

### Continuous real value function

34.12 Show that if f is a continuous real-valued function on [a,b] satisfying b &#8747; f(x)g(x) dx = 0 for every continuous function g on [a,b], then f(x) = 0 for a all x in [a,b].

### Basic exponential function graph

Why does the graph of the basic exponential function lie entirely above the x-axis?

### Horizontal asymptotes and costs

How could you interpret infinity in the y values for costs, a negative x value for time, or a horizontal asymptote in y values for profits?

### Determination of Horizontal Asymptotes

Please address the following: How do you determine horizontal asymptotes, if any, given the equation for a rational function?

### Parallel lines and equations

What is the solution to a system of 2 equations represented by 2 parallel lines in the same plane?

### Determine vertical & horizontal asymptotes & sketch graph

Determine the vertical and horizontal asymptotes and sketch the graph of the rational function F. Label all intercepts and asymptotes. F(x) = 1__ x + 4

### Resultant Force Component Methods

A=(310 LBS, 37DEGREES), B=(267 LBS, 348DEGREES), C= (148 LBS, 247DEGREES), D= (139 LBS, 167DEGREES) Determine the resultant force by the component method.

### Resultant force

Find the resultant force (sum) of these displacements: 400 mi, EAST: 200 km, EAST: 400 km : AND 100mi, NORTH.

### Forces Exerted on Vertical Angles

A steel beam exerts a force of 350 lbs against a wall at a 60 degree angle from vertical. What is the horizontal component of this force acting perpendicular to the wall?

### Resultant and Horizontal Force

What are the vertical and horizontal forces of a 1200 N force directed to the right and upward at an angle of 43 degrees with the horizontal?

### Riemann Integrable Function : Upper and Lower Sums

Please see attachment. Q. Show directly that the function is integrable on R = [0,1] x [0,1] and find (Hint: Partition R into by squares and let N , limUp = limLp = integrable Up = upper Riemann sum of f respect to partition &#61664; U(f,p) = Lp = Lower Riemann sum of f respect to partition &#61664; L(f,p) =

### Vector Components : Force

A FORCE OF 85 N ACTS TO THE LEFT AND DOWNWARD AT AN ANGLE OF 45 DEGREES WITH THE HORIZONTAL. WHAT IS THE EFFECTIVE DOWNWARD FORCE AND WHAT COMPONENT IS ACTING TO THE LEFT?

### Examples of Functions : Exponentials, Graphs and Usefulness

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function. Plot the graph of both the functions and post to the discussion forum. Discuss these functions and their graphs with your classmates. 2. Given the values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form each of the follow

### Graph of polar equation

Inspect the four given graphs, which are plotted in polar coordinates (and shown in an attached .doc file), and choose the graph that corresponds to the polar equation r = 6 - (cos theta).

### Functions : Pointwise Operations

If function f(x) = x^2-3x-4, find and simplify f(x+h)-f(x)/h

### Chromatic Numbers

Use words to describe the solution process. No programming. 2. Let G = (V,E) be a graph where V {1,2,3,4,5,6,7,8,9,10,11,12} and E contains all edges connecting to vertices a and b such that ab=0 (mod 3). What is the chromatic number of G? Is G planar? See the attached file.

### Graph Coloring Problem: Describe the Solution Process

Please use words to describe the solution process: Let G be a graph with exactly one cycle. Prove that x(G) is less than or equal t0 3. *(Please see attachment for proper symbols).

### Complete the Graph Problem

Please use words to describe the solution process: Let G be a graph with n vertices that is not a complete graph. Prove that x (G) < n HINT: If G does not contain k3 as a subgraph, then every face must have degree at least 4. *(Please see attachment for proper symbols).

### Graphs and Figures

Please use words to describe the solution process. Let G and H be the graphs in the following figure (see attachment): Please find x(G) and x(H). See the attachments.

### Evaluate the Binomial Coefficient

Evaluate the combination or binomial function in the completion 48 factorial over 37 factorial. The answer should equal to 22595200368.

### Lipschitz functions

A function f:A->R is called Lipschitz if there exists a bound M>0 such that Absolute value of f(x)-f(y)/x-y <=M for all x, y belong to A. Geometrically speaking a function f is Lipschitz if there is a uniform bound on the magnitude of the slopes of lines drawn through any two points on the graph of f. a- Show that if f:A->R i

### Writing Equations Distributive Property

I must write an equation that has the solution x = -2 and graph it. My equation must include combining like terms on the left side and distributive property on the right side. I missed two weeks of class due to illness, and am having a hard time working this out. I just need a sample answer or starting point so that I underst