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    Graphs and Functions

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    Intepreting Data and Piecewise Functions

    A factory begins emitting particulate matter into the atmosphere at 8 am each workday, with the emissions continuing until 4 pm. The level of pollutants, P(t), measured by a monitoring station 1/2 mile away is approximated as follows, where t represents the number of hours since 8 am: p(t)= 75t + 100 if 0 is less tha

    Differentiable Functions and Inverses

    1. Let be a differentiable function such that (0) = 0 and for all . a) Show that is strictly monotone and therefore its inverse exists. b) Assume that exists. Compute Please see the attached file for the fully formatted problems.

    Finding the Equations of Functions

    Find the equation for each of the following items below: a. A line that passes through (1,1) and is perpendicular to the line 3X+4Y=12. b. A line that passes through (5,4) and has a slope of 2. c. A line that passes through (9,8) and has a slope of -1. d. A line that passes through the points (1,2) and (12,24) e.

    Equations of Tangent Lines and Areas Between Functions

    Please see the attached file for the fully formatted problems. Determine the area between f(x) = 2x and on the domain determined by the points where the graphs of the functions cross. a. 0.1111 b. 1.0125 c. 1.6667 d. 1.3333 Find the function whose tangent line has the slope for each value of x, and whose grap

    MTH133: Unit 4 - Individual Project - B

    Please see the attachment for detailed description. 1) State the domain of the following: a) f(x) = sqrt (x - 8) b) h(x) = 3x^2 + 5x - 3 c) m(x) = 5/(x^2 + 9) d) l(x) = 5x - 4 e) g(x) = (7x + 4) / (x+4) 2) Suppose the graph of y = x^2 is shifted to obtain each the following graphs. What is the equation of the funct

    Graphs : Chromatic Number

    Show that the chromatic number of G_1 + G_2 isX(G_1) + X(G_2) for any two graphs G_1 and G_2. Where X(G)is the Chromatic Number. defn: X(G) a proper colouring or simply a colouring of the vertices of G is an assignment of colours to the vertices in such a way that adjacent vertices have distinct colours; X(G) is then the mi

    Graphs, Nodes and Partitions

    Suppose there are 90 small towns in a country. From each town there is a direct bus route to at least 50 towns. Is it possible to go from one town to any other town by bus possibly changing from one bus and then taking another bus to another town?

    Describing Curves and Graphs

    Describe in words the graph of each of these curves below. Include in your description the shape, along with other possible relevant information such as length, width, and center points. a. Y = 3X2 b. (X-1)2 + (Y-8)2 = 16 c. (X+2)2 + (Y-4)2 = 36 d. Y = X2 - X

    Evans Price Adjustment Model : Supply and Demand Functions

    Qn1)The Evans Price Adjustment model is a dynamic model in which price p denote the price of a particular commodity, S(p) and D(p) denote the supply and demand functions of that commodity respectively. These 3 parameters are regarded as function of time t. The time rate of change of price is assumed to be proportional to the sho

    Discontinuous Functions

    Find the values of f(x) at which each of the following functions is discontinuous. Why is the function discontinuous at that value? a) f(x)= {2x+5, x<1 {x+6, x is greater than or equal to 1 b) f(x)= {2x+5, x is not equal to 1 {3, x=1 c) f(x)= 1/x d) f(x)= {(x^2)+10}/{(x^2)-x-2}

    Maximum Value of a Function

    Suppose that a projectile is fired at an angle of 45 degrees from the horizontal.... Please see attachment and show work.

    Characteristic Function of Metric Space

    Let S &#8834; M. (a) Define the characteristic function Xs : M --> R. (b) If M is a metric space, show that Xs(x) is discontinuous at x if and only if x is a boundary point of S. [Please see attached PDF file for full problem]. for part (a), I think something similar to http://planetmath.org/encyclopedia/Characteristi

    Lines Parallel To y=-x+6

    Find an equation of the line that is parallel to the line y = -x + 6 and that passes through the point (5,9).

    Equation of a Line from a Graph

    Please see the attached file for the fully formatted problem. Write an equation of the line below. Do I have to calculate slope for both points?

    Vertical and Horizontal

    Write and equation for the vertical and horizontal lines passing through the point (4,-4) in (x,y) coordinates. Please show the steps to help me understand how you accomplished this.

    Graphing Word Problem

    Joe will drive to LA. The distance to his destination in miles is a linear function of his driving time in minutes. When graphed the function gives a line with a slope of -0.95. Joe hs 46 miles to his desitnation after 20 minutes of driving. How many miles will he have in his destination after 38 minutes of driving?

    Graphing Word Problem

    A montly cost of a long distance phone plan in dollars is a linear function of the total calling time in minutes. When graphed the funtion gives a line with a slope of 0.13. The monthly cost for 42 mintues of calls is $14.62. What is the monthly cost for 33 minutes of calls.