Share
Explore BrainMass

Graphs and Functions

A function is a relationship between inputs and outputs with a specific property that one input is related to only one output. The input of a function is usually denoted as x, while the output of x is denoted as f(x), which stands for ‘function of x.’ The input and output of a function can be described as an ordered pair. For example, consider the following function:

F(x) = x^2 + 3x + 2

If the input x was 1, then the output would be

F(x) = (1)^2+3(1)+2 = 1+3+2 = 6

Thus, the ordered pair can be written as (1,6)

If the input x was 2, then the output would be 12, and the ordered pair would be (2,12)

In mathematics, the graph of a function is just an illustration of all the ordered pairs. So for the above equation, (1,6) and (2,12) as calculated previously would be plotted. Other ordered pairs for the inputs 3, 4 and 5 are calculated below:

(3,20)

(4,30)

(5,42)

With these ordered pairs, a simple plot can be graphed to show the general relationship between the input and output of a particular function. Thus, understanding the rules and properties of functions, as well as how to graph them, is particularly important in the discipline of Algebra.

Equation of a Line Tangent to a Circle

(a) Consider the circle that has its center at the point (2, -3) and passes through the point (5, -1). Find the radius of this circle, and find the point-slope and slope-intercept forms of the equation of the line which is tangent to this circle at the point (5, -1). In your solution, use only algebra and the fact that a line wh

When do I need absolute value when simplifying nth roots?

In a radical, root expression with an exponent inside, on the radicand or a factor of the radicand, is equal to an even number index, then we need use absolute value in our answer answer. Possibly, this simplifies out, depending on other conditions. What are the rules and reasoning for this?

Polynomial Identities

Polynomial Identities and Proofs Essential Questions: • How can polynomial identities be proven? • What can polynomial identities apply to beyond just polynomials? It's time to show off your creativity and marketing skills! You are going to design an advertisement for a new polynomial identity that you are going to i

Equation of closed curve in x-y plane and its parametric form

The equation 49x^2 + 36y^2 = 1764 describes a certain closed curve in 2-dimensional space. (The caret (^) indicates that the variable to the left of the caret is to be raised to the power to the right of the caret. That is, "x^2" means "x squared" and "y^2" means "y squared".) Determine the type of closed curve this equation

Radical Function and Rational Function

MATH133 Unit 4: Functions and Their Graphs Individual Project Assignment: Version 2A Name (Required): __________________________________________________ IMPORTANT: Please see Question 3 under Problem 2 for special instructions for this week's IP assignment. This is mandatory. Show all of your work details for these calculati

Interpreting Graph Data

Graphical Methods 1. What interval represents the most number of courts? 2. How many courts have less than 20,000 seats? 3. How many courts have between 17,000 and 19,000 seats? 4. How many courts have at most 20,000 seats? 5. How many courts have at least 21,000 seats? 6. How big is each interva

Dilations Ordered Pairs Coordinares

Write the ordered pairs for each coordinate. Use the scale factor to determine the coordinates of the transformed figure. Write the ordered pairs using arrow notation and graph the dilated image. See attached file for graphs to go along with each problem.

The solution gives detailed steps on answerting 14 short questions regarding on probability calculation assuming the normal distribution. All questions are explained in details.

For the following answer True or False for each question 1. A population forms a normal distribution with µ=80 and ơ=10. In this population, 69.15% of the scores greater than x=75. 2. A population forms a normal distribution with µ=80 and ơ=10. In this population, 84.13% of the scores greater than x=90. 3. A population fo

Stationary point

This question concerns the function f(x)=x^3 +3x^2 −24x+40. (a) Find the stationary points of this function. (b) (i) Using the strategy to apply the First Derivative Test, classify the left-hand stationary point found in part (a). (ii) Using the Second Derivative Test, classify the right-hand stationary point found in part

Completing the Square, Quadratic Functions, Axis of Symmetry, and Intercepts

1. Using completing the square to describe the graph of the following function. Support your answer graphically. f(x) = -2x^2 + 4x + 1 2. Graph the function: g(x) = (x-2)^3 3. Determine the quadratic function f whose vertex is (3, -2) and passes through (2, 1) 4. Graph the line containing the point P and having slope m: P

5 Questions on Graphing Quadratics and Inequalities

1. Find the intercepts of the graph of the equation Y=x2-4 X2-9 The intercepts are______(type ordered pair,using intergers or fractions) 2. Analyze the graph of the function R(x) =x+9 x(x+18) a) What is the domain of R(x)? b) What is the equation of the vertical asymptotes of R(x)? X=_____ (type integer

Functions domains and range

1. Find the average rate of change of f(x)=x^3-9x+9: a) from -8 to -2 b) from -1 to 1 c) from 1 to 4 a) What is average rate of change of f (x) =x^3-9x+9 from -8 to -2? 2. The function f is defined as follows f(x) = {4+2x if x<0 {x^2 if x>0 a) Find the domain of the function b) Locate any

Function and Its Domain

1. Determine whether the following relation represents a function. If the relation is a function then state domain and range? {(4,6),(-2,6),(7,8),(4,13)} Does the given relation represent a function? 2.Determine whether the following relation represents a function. If the relation is a function then state domain and range?

Finding a rational function with specified properties

Asymptotes for rational functions: f(x) = P(x)/Q(x). Given the formula, reconstruct a rational function based on the following pieces of information: 1. The rational function has two vertical asymptotes and one oblique (slant) asymptote. 2. One vertical asymptote is at x = - 5 3. The second vertical asymptote, which crosses

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

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

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

Optimal Path

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

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

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