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Graphs and Functions

Usefulness of composite functions

Composite functions are useful when one quantity depends on a second quantity, and in turn that second quantity depends on a third quantity. This is an extremely general situation with lots of real-world applications. 1. The cost of getting new life insurance depends on how old you are, and how old you are depends on what

Graphical Representations of Different Functions

1. Use the graph of f(x)= x^ to match the function to its corresponding graph. In words describe the transformation that occurs (ex: The graph of f(x) is shifted 6 units to the left). F(x) = x^ Give the following functions and Description of transformation and plot the graph of each. a) G(x) =

Functions, Zeros And Application

Given f(x) = ex2 + fx + g, where e, f, and g are real numbers, (a) Find the zeros of the function in terms of e, f, and g. (b) Under what condition would the zeros of the given function be two distinct real values? (c) Determine the x-coordinate (the x-value) of the point that would represent the minimum or the maximum of the

Weekly Dollar Demand and Supply Functions for Tents

The weekly dollar demand and supply functions for tents, t, are given by the following respective formulas: D(t) = -0.1t^2 + t + 40; S(t) = 0.1^2 + 2t + 20 a) We wish to graph D(t) and S(t) . Answer the questions below. b) At what price will there be demand for tents? c) At what price will there be no supply of t

How to Graph Lines in the Math Lab

For the problem: Graph the linear function. f(x) = 5x - 2 Use the graphing tool to graph the line. As in the attached image, a student will find a problem graphing the line using any two points, with the intercepts being the most obvious.

Gradient, Divergences, and Curl

Gradient: 1. Find the gradient of the function f : x^2y/ z at the point M(-2;3;4). What is the directional derivative of this function in the direction of vector I =(12;-4;3)? 2. Find the gradient of the scalar function f = cos(|r|^n) , Where r : (X, y, Z). Write the result as a function of r 3. Find the normal line t

Mathematics: Fundamental Questions on Slopes/Gradients

1. Identify whether the slope is positive, negative, zero or undefined. Please show work or explain answer so that I can understand it Please see attachment for graph for question 1. a) Positive b) Negative c) Zero d) Undefined 2. Find the x- and y-intercepts for the equation. Then graph the equation. Please show work.

Solving Quadratic Equations and Graphing Squares

Section 8.2 #12 solve each equation by using the quadratic formula (what is this quadratic formula? Don't understand how this is done) M^2 + 2m = 8 #20 Solve each equation by using the quadratic formula 4 + 20x = 25x^2 #28 solve each equation by using the quadratic formula 2y^2 + 1 = 2y #42 Number solutions. Find b

Linear Models: Compare the Profits and Evaluate

Please help find linear values for Company A and B. (The question is formatted in the attachment). Two companies start up at the same time. Company A claims their annual profits follow a linear model, P(x)=10x-7 where x is the number of units sold and x≥1. Company B claims that their annual profits follow a radical model, P

Composite Function Problem: Cost

Hi Changping: Can you help me with this composite function question? Composite Function: The cost for all bases is L=4x+6, where x is the cost of employees, one step further, what if the cost of employees x varies with the troop level, t, and x=2t+5. What would be the cost of the bases in terms of the troop levels? Than

Assessing Graphs and Functions

Set 3 #34 Function expressed by ordered pairs: determine whether each relation is a function [(2, -5), (2,5) (3, 10)] #36 [(3,6), (6.3)] #90 Function notation: left f(x) = 3x -2, g(x) = -x^2 + 3x - 2, and h(x) = |x + 2| evaluate each expression f(100) #92 g(-3) #94 h(-19) #106 Perimeter of a square. Find a formu

Solving Inequalities for a graph

Help solve the following High School Math 1. Y/-6 < 10 (Solve the inequality). 2. h -2 < 1 (Solve the inequality. Graph the solutions) 3. r/6 (less than or equal to 3) solve the inequality. 4. C < 5 (Graph the solutions of the inequality on a number line) 5. Together, Louisa and Jill scored more than 30 points in the

Graphical Representations

Search the internet to find two graphs to critique: one you evaluate to be a good graphical representation of the information presented and the other to be a poor graphical representation of the information presented. Answer the following questions about your selected graphs. a. What types of graphs are used to displa

Non-Ideal Diode Equation (Saturation Current and Energy Gap)

Preamble It can be shown that the reverse saturation current in a diode is given by the equation: Is= BT^(2/3) exp (-Eg/NkT) where B is a constant that involves the physical properties, doping and geometry of the junction T is the absolute temperature Eg is the energy gap of the semiconductor in joules k is the Bolt

Price-Demand/Revenue Function

Scenario: A camera manufacturer producing a low cost digital camera has found that: Price-demand function p(x)=94.8-5x Revenue function R(x)=x*p(x)=x(94.8-5x) When price is in dollars and x is in millions of cameras sold, and revenue is in millions of dollars. a) What is the marginal revenue equation? b) Find the output

Pairs: Functions or Non-Functions

Solving Equations with Two Variables: I need to know if each of these example pairs is a function or a non-function and why. y = -2x + 3, y = 2x +2, y = 4 and x = 3. Thanks Cheryl

Optimal Path

A maximum flow problem to find the maximum amount of water to flow from city 1 to city 10.

Graphing Polynomial and Rational Functions

Sketch the graph of the polynomial function f(x)= x^4-2x^3-2x^2+6x-3 including leading term to graph behavior, listing domains, y-intercepts, label exact values of zeros, their multiplicities and the behavior at the x-intercepts. Give relative minimum or maximum points.

Evaluating Investment Opportunities

Scenario: Welte Mutual Funds, Inc., is located in New York City. Welte just obtained $150,000 by converting industrial bonds to cash and is now looking for other investment opportunities for these funds. Based on Welte's current investments, the firm's top financial analyst recommends that all new investments be made in the oil

Evaluating functions and finding x-values

Please show all steps and related work! Thank you for helping me! Evaluate the function when x = -2, 0, and 3. (1) m(x) = -6.5x (2) s(x) = 2/5x + 3 (3) h(x) = 3/4x - 6 (4) Given f(x) = -6.8x + 5, what is the value of f(-2)? Find the value of x so that the function has the given value. (5) g(x) =

Fahrenheit and Celsius

7. The formula C=5/9 (F-32) , where F is equal to or more than -459.6, represents Celsius temperature C as a function of Fahrenheit temperature F. (a) Find the inverse function of C. (b) What does the inverse function represent? (c) What is the domain of the inverse function? Validate or explain your answer using the

Finding the value of x and rates of change

1) Please find the value of "x" so that the line passing through the two points has the given slope. (x, 7) and (2, -3), m = 5/2 2) The table shows the temperature for 4 days. Find the rates of change in temperature with respect to time during each of the time periods. Date 10/10 10/12

Graphing a function, number of circuit boards

People assigned to assemble circuit boards for a computer manufacturing company under go on the job training. From past experience it was found that the learning curve for the average employee is given by: N=40(1-e^-0.12t) (everything past e is to the power) where N is the number of boards assembled per day a

Graphing a rectangular coordinate system

Revenue, The marketing research department for a company that manufactures and sells "notebook" computers established the following price-demand and revenue functions. p(x)=2,000-60x (price demand function) R(x) = xp(x) (revenue function) =x(2,000-60x) Where p(x) is the wholesale price in dolla

Automobile Production: Table, Graph and Modeling

The table shows the retail market share of passenger cars from Ford Motor Company as a percent of the US market. Year Market share 1980 17.2% 1885 18.8% 1990 20.0% 1995 20.7% 2000 20.2% 2005 17.4% A mathematical model for this data is given by f(x) = -0.0206x^2

Determining the Nearest Integer

Use the following graph of a function f to determine x or y to the nearest integer as indicated. Some problems may have more than one answer... Here is the information on the graph: Where Y would be is f(x) Y=f(x) if you have your box and have 10 sets on each line, I will start on the 5th set on the lower left side. T

Which of the Indicated Correspondence Defines Functions?

Let P be the set of patients in a hospital, let D be the set of doctors on the hospital staff, and N be the set of nurses on the hospital staff. Which of the indicated correspondence defines functions? Explain. (A) a patient corresponds to the doctor if that doctor admitted the patient to the hospital. (B) A patient corres

Solution graphs of linear systems

Consider the linear system x' = Ax, where A is a n x n real matrix. If x = x(t) is a solution of the linear system, we define: G(x) = {x(t) : t E R), which is the set of points on the solution curves x=x(t) in R^n. The set G(t) is called the graph of x = x(t) . Show that if x(1) = x(1)(t) and x(2) = x(2)(t) are any two

Making Proper Graphs

Read the article "How to Display Data Badly," by Howard Wainer. It was published in the American Statistician in 1984, volume 38, pages 137-147. You can find it here:http://www.jstor.org/stable/2683253. Next, scour the Internet (or if you are feeling particularly plucky, look through your company's annual report!) to find an

Income Distribution Diagrams

A study of family income is studied through a sample of 500 randomly selected families. The results can be summarized as the mean family income was $41,000 and the median income was $29,000. The highest income was $253,000 and the lowest was $2,600. Part 1) Sketch a diagram of the income distributions. Describe if the dis