Share
Explore BrainMass

# Graphs and Functions

### Imaginary solution

Find the imaginary solutions to each equation. 3y^2 + 8=0

### Find the interval on which the function

See attached file for full problem description. Find the interval on which the function 2 2 ( ) ( 2) ( 3) f x x x = &#8722; + is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.

### Problem set

Question 1 Consider the functions f(x) = x^2 and g(x) = square root of x, both with domain and co-domain R+, the set of positive real numbers. Are f and g inverse functions? Give a brief reason. Question 2 Given the Hamming distance function f: A X A -> Z defined on pairs of 8-bit strings, (where A is the set o

### Exponential, logarithmic functions, etc

Refer to the graph given (attached) and identify the graph that represents the corresponding function. Justify your answer. y = 2x y = log2x

### Measurable Functions

Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x. Please make sure to show the proof in both directions.

### Value of function at a given point

1. The number of 4-year college, public and private, in the period 1980-1996 can be modeled by f(x)=0.0003x^3 - 0.007x^2+0.058x+1.957 0 less than or equal to X less then or equal to 16 Where X is the number of years since 1980 and f(x) is the number of 4-year colleges measured in thousands. Determine the average number

### graph the functions with data points

For the function, y = ___1____ x - 2 a) Give the y values for x = -2, -1, 0, 1, 2, 3. Answer: Show work in this space. b) Using these points, draw a curve. Show graph here.

### In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?

In the real world, what might be a situation where it is preferable for the data to form a relation but not a function? I found the formula that converts temperature in degrees Celsius to temperature in degrees Fahrenheit. It gave me the following data points: Fahrenheit Celsius Freezing point of water 32 0 Boiling po

### Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a(x - h)^2 + k.

Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k. Using the vertex, x-intercept and y intercept The vertex x=h split the graph into two halves. So, drawing the vertical line x=3 and graph. On the graph the curve turn at the vertex ( 3,-

### Graphs and Solving Linear Equations Word Problems (20 Problems)

Solve the following equations for the unknown. 1. 5x = 20 2. 7x - 3 = 18 Graph the following equations; calculate the slope, x-intercept, and y-intercept, and label the intercepts on the graph. 3. y = x + 3 4. y = -2x - 7 5. 2x + 3y = 9 6. A consumer electronics c

### Understanding the Ellipses, Parabolas, Hyperbolas from basics to more advanced level- all in one assignment!

1 The equation xsquared + ysquared =1 represents an ellipse. ________ ________ 25 169 a) State the lengths of the major and the minor axes. b) State the x-intercepts and y-intercepts. c) Find the coordinates of loci. d) Find the points of intersectio

### Break even analysis: Labor intensive firm and capital intensive firms

Draw two break-even graphs-one for a conservative firm using labor-intensive production and another for a capital-intensive firm. Assuming these companies compete within the same industry and have identical sales, explain the impact of changes in sales volume on both firms' profits. Although no example is provided in the

### Equations of Straight Lines

1. Graph line with equation y=-4x-2. 2. 2x=8y=17=0 3. Graph the line with slope -2 passing through the point (-3,4). 4. Find slope of the line graphed (-44, 28) (9, -12). 5. x=9 graph the line 6. 6x-9y+7=0. 7. 2x=5y+3 8. Write an equation of line (0, -4). 9. A line passes through the point (6, -6

### Asymptotes, Descartes's Rule and coordinates of the vertex

1. f(x) = x^3 + x^2 - 4x - 4. (a) What is the end behavior of this function? (Does it go up or down to the left? Does it go up or down the right?) (b) What is the maximum number of turning points for this function? 2. Give the coordinates of the vertex of the parabola y = (x + 2)^2 + 5. 3. Use Descartes's Rule of Sig

### Simplifying and Solving Equations with Exponents

1. Simplify the expression using properties of exponents. Answer should contain positive exponents only. (3x^2y^3)^2(3xy)^2 / (2x^4y^3)^-3 2. Solve for X: 3/x - 1/x+2 = -2/3x+6 3. Use the quadratic formula to solve for x: x^2 -4x + 2 = 0 4. Solve for x by factoring: x^3 + x^2 - 6x =

### Euler Function

(See attached file for full problem description) Conjecture: Suppose that m and n are positive integers. If gcd(m,n)=1, then . a. If m and n are positive integers and k is any integer, show that gcd(k,mn)=1 if and only if gcd(k,m)=1 and gcd(k,n)=1. b. Suppose gcd(m,n)=1. Prove that establishes a bijection between

### Exponential Growth and Decay Projects

Think of one real situation that involves exponential growth and that involves exponential decay. for each example, your project should include the following: * Paragraph - Briefly explain the situation. You may make up your own information, but make it realistic. Include the facts needed to write an equation. * Equation -

### Real-Life Applications of Hyperbolas and Parabolas

One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing

### Uniformly Continuous Functions and Mean Value Theorem

Assume that f is differentiable for each x and there exists M>0 such that for each x Prove that f is uniformly continuous on D. Hint: Can use the mean value theorem. keywords: differentiability, continuity

### One-to-One and Onto Functions

Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X → Y is one-to-one and the function g : X →Y is onto. (i) Use the function f to show that m ≤ n. (ii) Use the function g to show that m ≥ n. (iii) Is f : X → Y onto? Justify your assertion. (iv) Is th

### Input-output Tables and Equations of Lines, Slope and Intercept

Decide whether the relation is a function. 1- (6,5), (4,3), (-2,3), (0,-1) , (-1,2), (-4,-5), (-3,4) 2- (4,4), (3,3), (-1,1), (6,6), (1,-2) make an input-output table for the function rule. Use a domain of -10,-5,0,5, and 10. Identify the range. y=8x+1 y=-6x y=x square 2+5 write a function that relates and x and

### Foci, asymptotes and graph of a given hyperbola and finding the point of intersection with a given line.

A hyperbola is given the equation x^2/25 - y^2/9 = 1 A) Find the coordinates of the foci and the equations of the asymptotes. B) Find the point of intersection with the line y=4-x c) Graph the hyperbola, the line, and the point of intersection. Please explain how to graph this because I dont understand it and

### Domain values

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

### Examples of Arithmetic series and sequence

Details: Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadrat

### Volume function

The volume of a cylinder (think about the volume of a can) is given by V = &#960;r2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function of r.

### Algebra Description Graphed

Please answer the following questions ASAP: Match each description of a graph with an equation. The graphs are all described in relation to the graph y = x^2 shifted 3 units upward shifted 3 units to the left shifted 3 units downward stretched out and flipped upside down shifted 3 units to the right

### Graph for rational function

Given the information in the attachment, please sketch the graph.