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Graphs and Functions

Functions : Asymptotes, Intercepts, Maxima and Minima

Please see the attached file for the fully formatted problems. 1. Find the vertical asymptote(s) of F(x) = A. x = 1/3 B. x = 3 C. x = 0 and x = 3 D. None 2. Find the horizontal asymptote of F(x) = A. y = 5 B. y = -1 C. None D. y = 0 3. Find the horizontal asymptote of F(x) =

Catenary Equation of a hose.

Hi, Given are the elevations of a hose connected to a building on one side and to a ship on the other. The below attached sketch shows the POC-Points of Connection as 19.09 ft on building and 49.9 ft on the ship. The distance from the building to the mid-span of hose is r2= 5 ft and r1 from ship is r1=6.5 ft. The hose is not

Graphing : Line Equations, Slopes and Intercepts

Please see the attached file for the fully formatted problems. 1.) Given the function f described by f(x)=x+7, find each of the following. F(0)=______ F(-15)=______ F(-6)=______ F(5)=______ F(b+6)=______ 2.) Find the intercepts, and then use them to graph the equation. Y= -5 - 5x 3.) Graph the equation using the slope

Graphs : Equation of Line, Midpoints and Line Segments (20 Questions)

Please see the attached file for the fully formatted problems. 1.) Find the distance between the points (4,-1) and (-5,3) 2.) Find the midpoint of the line segment with endpoints (5,-2) and (-3,12) 3.) Graph the equation 4.) 5.) Find the equation of the line with slope 0 and y-intercept (0,-2). Write your answer in t

Functions and Graphs : Sketching, Domain, Range and Asymptotes

Please see the attached file for the fully formatted problems. 1. The length of a rectangular field is 3 times its width. If fencing costs $12 per metre, express the cost, C, of fencing the field as a function of the width, w. 2. Draw a set of axes and then plot the graph of the function f(x) = 2x ?4, for ?3<x<5. 3. (i)

Exponential and Logarithmic Functions

1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case. 2. A cell divides into two identical copies every 4 minutes. How many cells will exist after 3 hours?

Find a linear function that fits the given data

The table list data - Average Salaries of Athletes in 1991 and 2001 Use the data points to find a linear function that fits the data and then use the function to predict the average salary in 2005 and 2010. Year average salary 1991 $273,000 2001 $1,420,000

Lower semi-continuous and convex function

These are problems that ask as to which values of a variable a function is a) convex and b) lower semi-continuous. Please see the attached file for the full question.

Critical points

Determine the critical points of the function: f(x1, x2) = (2 - x1 - x2)^2 + (1 + x1 + x2 - x1*x2)^2. Try to decide their nature.

Equation of Parabola

A. Write an equation for a parabola with a vertex at (0, -5). HINT: Assume the parabola is in the form ax^2 + bx + c = y. Need to solve for a b and c. b. Is there more than one parabola that has this vertex? c. What happens to your parabola if you change the constant term to 12? d. What happens if you doub


Please help with circled questions. thanks Find a formula for the inverse of the function. Use the given graph of f to sketch the graph of f^-1. Find the exact value of log_8 2

Precalculus word problem

Background: You are the financial manager of a furniture company. It is your job to create supply and demand graphs that show the break-even point for the company. The functions that describe how the company can break even will be represented with linear equations. Linear inequalities will be used to graph conditions where the

Position graph

See attached Shown are graphs of the position function of two runners, A and B, who run a 100-m race and finish in a tie. a) Describe and compare how the runners run the race. b) At what time is the distance between the runners the greatest? c) At what time do they have the same velocity?

Solve an equation

Solve: 5/8x + 1/16x = 3/16 + x The solution set of the equation is { } Simplify the answer.

Quadratics: Graphing a Parabola

Task: Please graph the following parabola: y=(1/5)x^2-2x+9 To graph the parabola, plot the vertex and four additional points, two on each side of the vertex.

Systems of equations

1.Solve the system of equations by graphing. Then classify the system x +y=11 x - y=1 What is the solution of the system of equations? ____________________ (Type an ordered pair . Type N if there is no solution. Type R if the solution is all real number.) Is the system consistent or inconsistent? A.)___________inconsisten

Discontinuous functions

See circled problems on attachment Explain why each function is continuous or discontinuous. Explain why the function is discontinuous at a=1. Sketch the graph of the function

Solving and Graphing Equations

See attached 1. a. Solve b. Find the x-intercepts of 2. Determine the nature of the solutions of the equation 3. Find and label the vertex and the line of symmetry. Graph the function 4. The width of a rectangle is 3 ft less than the length. The area is 4 ft . Find the length and the width. 5. For the scatter

Equations and graphing

Please help with work and answers. a) Calculate the value of the discriminant. b) By examining the sign of the discriminant in part a, how many x-intercepts would the graph of have? Why? 6) a) Find the corresponding y values for x = -4, -3, -2, -1, 0, 1, 2 if . b) Use Microsoft Excel to plot the points found in part a a