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    Graphs and Functions

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    Slopes and Intercepts

    I need to graph a line containing the given pair of points and find the slope. (2, -4), (-3,2) Find the slope of a treadmill 0.4ft tall and its five feet wide. In order to meet federal standards, a wheelchair ramp must not rise more than 1ft over a horizontal distance of 12ft. Express this slope as a grade.

    Production Functions and Variable Costs

    1) In the production function, suppose that z2 is 12. The total product function is TP(z1)= 120(z1)^1/2 Find the average product function? Answer: AP(z1) = TP(z1)/z1 AP=120/(z1)^-1/2 Could you explain in detail why this is the answer. 2. Could you explain how to find Variable Cost VC(y) and if possible could you

    For the set of scores calculate the requested values

    1. For the set of scores calculate the requested values. Scores: 2 5 3 6 4 a.{X b.{x^2 c.({X)^2*5 2. For the set of scores calculate the requested values. X Y 8 -1 11 3 2 5 3 -4 a.{XY b.{X{Y ({XY)^2 d.{(x-1)^2{Y+3)^2

    Cost Functions

    If the marginal cost of producing x units is given by 20 - 0.04x , and the fixed cost is $100, determine the cost function C(x).

    Exponential and Radical Expressions Problem Set

    While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign. Please provide sources used. 1) Solve the following e

    Radicals

    Solve the following equations. a) Answer: Show work in this space. b) . Answer: Show work in this space. c) . Answer: Show work in this space. 2) Is an identity (true for all values of x)? Answer: Explain your answer in this space. 3) x -2 -1 0 1 2 y .25 .

    Inverse functions derivatives

    Use the derivative to determine whether the function is strictly monotonic on its domain and therefore has an inverse function. f(x) = x^3 -6x^2 +12x

    Inverse functions

    Show both analytically and graphically that f and g are inverses: f(x) = 3-4x g(x) = (3-x)/4

    Graph Characteristics of Functions

    (See attached file for full problem description) use the function f (x) shown below to answer the questions. 1) Determine where the function f is increasing and where it is decreasing. 2) Determine all relative extreme points of f. 3) Determine where the graph of f is concave up and whe

    Construct a graph

    (See attached file for full problem description) The function that describes first-class mail postage has discontinuities. The cost of first-class mail is 37¢ for the first ounce (or less) and then 23¢ for each additional ounce above that. Make a graph showing the total cost of postage for packages up to 4 ounces.

    Rearranging equations graphs

    How would you rearrange each of the following equations and make a mapping rule for each one so that they can be graphed? 2 a) y = -1/2 (x + 4) - 1 2 b) 1/3 (y + 5) = (x - 2) (Note - (x+4) is squared, as well as (x-2). Couldn't find proper s

    Convex and Compact Sets and the Implicit Function Theorem

    5. Consider the set S = {(x_1, x_2) belongs to R^2: x_1 + x_2 = 1 and x_1 > 0, x_2 >= 0}.Prove that S is convex and compact. 6. Consider the function: F(x_1, x_2, y) = (x_1)^2 - (x_2)^2 + y^3. a) Show that the equation F(x_1, x_2, y) = 0 defines y as an implicit function of x_1 and x_2 near the point (x_1, x_2) = (6,3).

    In Exercises 1-4, the graph of a function f is given

    In Exercises 1-4, the graph of a function f is given. Tell whether f appears to be periodic. These are problems that deal with the concept of periodic function. Find the fundamental period & amplitude, etc. Full problem in attached file.

    GRAPHS and COMPOUND INEQUALITY

    I need to graph the solution set to each compound inequality. 1. x > - 2 and x < 4 (Please note that this symbol < is underlined) sorry I don't know how to do the underlining. I need to graph each compound inequality for this problem 2. 3 - x < y + 2 or x> y + 5

    Graphing and Solving Equations

    1. Evaluate. (-8)2 - 19 A) 45 B) -83 C) -35 D) -45 2. Solve and graph the solution set. 4x + 9 &#61619; 3x + 16 A) -7 0 B) 0 7 C) -7 0 D) 0 7 3. An arithmetic student needs an average of 70 or more to receive credit for the course. She scored 67, 74, and 63 on the first three exams. Write

    Inverses

    Find the inverse of the function: f(x)=x^2+2x-1, x>0

    Collinear Points

    1. Use the Concept of slope to find t such that the three points are collinear. 1)(1,-4),(t,3),(5,10) 2. Find an equation of the line that passes through the given point and has the specified slope, and find three additional points through which the line passes. 1)point:(2,-1) Slope:m=1/4 2)point:(0,-5) Slope:m=3/2 3.

    Determine the Largest Size N For Each Function

    For each function f(n) and time t in the table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds. Show all work in detail. (see chart in attached file)

    Maxima, Minima and Critical Points

    For the following function, find the critical points, determine their nature (maxima, minima, inflection, etc.) and sketch it: g(x) = |x|*exp(-|x-1|)