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Graphs and Functions

Piecewise Functions

F(x) = {x if 0<= x <=1} {2-x if 1< x <=2} {0 if x > 2} Define a new function g, whose domain consists of all numbers x such that 0 &#8804; x &#8804; 4, and whose value g(x) for such x is given as follows: g(x) = the area between the graph of the function f and the horizontal axis from 0 to x. Problem: Find a f

Connected Graphs

Let G be a graph of diameter at least three. Can you find an upper bound on the diameter of the complement of G? Prove your findings! Let G be a connected graph and sq(G) be a graph which contains all vertices and edges of G and moreover edges joining every pair of vertices that were in G at distance 2. In other words, xy is

Finding Slope

Find the slope of the line that goes through each pair of points: (-5, -2) and (-2,1). What is the steepness of the line? (i.e. 3 units up and 5 units right)

Cylindrical Coordinates

What are the cylindrical coordinates of the point whose rectangular coordinates are x = - 4 , y= 2, and z = 4 ? r = (20)^(1/2) theta = z = 4 *need help finding theta in radians*

Finding the Equation of a Line

Find the equation of the line through each given pair of points. Write the answer in standard form using only intergers. (3, 5), (8, 15)

Function Expressing Volume of a Cardboard Box

A cardboard box manufacturer wishes to make open boxes from rectangular pieces of cardboard with dimensions 10 in. by 17 in. by cutting equal squares from the four corners and turning up the sides. (a) Find a mathematical model expressing the volume of the box as a function of the length of the side of the square cut out. (b)

Graphing Linear Equations

Graph the equation and identify the y- intercept 1. y = x + 3 2. 6x - 3y = 9 3.Find the absolute value. Erin left a 15% tip for a meal. The toal cost the meal, including the tip, was $21.16. What was the cost of the meal before the tip was added?


What do all the points on the vertical axis of a graph have in common? For each equation, find the intercepts. Then use the intercepts to graph the equation. 4x - 3y = 12 -3x = 6y -2 -3x + 12 = 0 Please see the attached file for the fully formatted problems.

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

Inverse functions

Use a graphing utility to graph the function. Determine whether the function is one-to-one on its entire domain. f(x) = 5x square root x-1

Inverse functions

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 that both f(x) and g(x) can be shown analytically and graphically: f(x) = 1-x^3 g(x) = 3 cube root 1-x

Inverse functions

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

Function f

(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.

Graphing equations and using mapping rules

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

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.


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