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Graphs and Functions

Constructing a Histogram

Use the frequency chart on the age of actors and when they won a prestigious award and construct a corresponding histogram. Age No. of actors 20-29 0 30-39 10 40-49 14 50-59 6 60-69 4 70-79 2

Determining Inverse Functions and Relations

I've attached a problem set which contains the following questions related to inverse functions. Can you help explain the concepts to me? Given point P of the function f(x), state the corresponding point P' in the inverse of the function. Determine if the inverse of each relation graphed below is a function. Find the inver

The Linear Function of a Spring

The distance d between a fixed spring and the floor is a linear function of the weight w attached to the bottom of the spring. The bottom of the spring is 18 inches from the floor when the weight is 3 pounds and 10 inches from the floor when the weight is 5 pounds. A. Find a linear equation that expresses d in terms of w. B. F

Graphing Sample Problems

Please help with the following problems. 1. Express each function graphed in terms of a base function. 2. Sketch the graph of a function based on a given base function. For example: Given f(x), sketch: f(x+3). See the attached file.

Determining equations for simple graphs

Please provide an example in determining an equation for a simple graph by determining the equation relating T to t on the attached file. Please use as many comments as possible.

Decay Function, Growth Function, and Intercepts

"For a decay function, there will be higher values of the y-intercept initially. For a growth function, there will be lower values of the x-intercept initially". Did this mean to sayy intercept for both of these? There is no x intercept, right? Also, won't the y intercept be (0,1) for both of these types of functions general

Newton's Method in Graph

Use Newton's Method to approximate the zero(s) of the function. Continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results f(x)=x-2sqrt(x+1). See the attached file.

Annual profit in thousands of dollars is given by the function

Annual profit in thousands of dollars is given by the function, P(x) = 100*sqrt(x - 5) + 3000, where x is the number of items sold, x ? 5. 3. Find the profit for 6 different values of x (show your work). PLEASE use x = 5, 69, 105, 230, 366, and 489 and make a table using Microsoft Excel.

Rational Curves

(a) Verify that 18^3 - 1^3 = 17 â?¢ 7^3 and find a point on the curve x^3 + y^3 = 17 with rational coordinates. (b) Make use of the point in (a) above to find a point on the curve X^3 + y^3 = 17 with positive rational coordinates.

Finding the critical points of the following functions

Find the critical points of the following functions and determine whether they are local maximums, minimums or otherwise using the second derivative test. If the second derivative test does not work, decide by computing the slope on either side of the point in question. (a) f ( x ) = x^2 + 12x + 36 (b) g( x ) = (x+3)^4 (c)

Simplification of Inverse Functions

I need some help with how to answer this question: Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverse of each other: f(x)=8x+8 and g(x)= x-8/8 a) f(g(x))= (simplify) b) g(f(x))= (simplify) c) f and g are inverse or are not inverse of each other

A rental company charges $40.00 a day...Solve equations.

A rental company charges $40.00 a day plus $0.34 per mile to rent a moving truck. The total cost, y, for a day's rental if x miles are driven is described by y = 0.34x + 40. A second company charges $32.00 a day plus $0.44 per mile, so the daily cost, y, if x miles are driven is described by y = 0.44x + 32. The graphs of the two

Finding Out the Slope and Y-Intercept

Solve without graphing. Find the slope and the y-intercept for the graph of each equation in the given system. Use this information (and not the equations graph) to determine if the system has no solution or an infinite number of solutions. y=1/8X+4 3X-Y= -4 The slope of the line y=1/8x +4 is?

Construct a stem and leaf plot of the data

The number of surfer's special burritos served was sampled during a dinner period 5:00 p.m. - 8:30 p.m. at a taco shop on a weekday. Below is the sample: 36 21 15 42 27 6 36 33 15 45 60 42 7 63 42 54 60 17 Construct a stem and leaf plot of the data.

Bearings and Kinematics

After t hours on a particular day, a freight train is s(t) = 20t^2 - (4/3)t^3 miles due east of its starting point (for 0 ? t ? 18). a) Where is the train (relative to its starting point) after 13 hours? b) What is the velocity of the train after 13 hours? c) What is the acceleration of the train after 13 hours? d) Is the tr

Function Definition and Examples

1. In your own words, define the word "function." 2. Give your own example of a function using a set of at least 4 ordered pairs. The domain will be any four integers between 0 and +10. The range will be any four integers between -12 and 5. Your example should not be the same as those of other students or the textbook. There a

Rational Functions

I need some help instructing me how to complete the following questions: Part 1: From a 220 feet high lighthouse in the Bahamas island of Nassau, a person sees a ship on the horizon. Due to the curvature of earth, how far is the ship from the lighthouse? Use the formula: d = sqrt[3h/2], where d is the distance in nautical

Graphing a utility function with exponents and calculating Marginal Utility

a) With a utility function of U(S,A)= S^0.4*A^0.6, derive a set of data points for U=1 and then plot a graph to show this indifference curve. Hint: use maximum values of 9 apples (A) and 27 sandwiches (S). b) When U=1, and using a maximum value of 27 sandwiches (S) and 9 apples (A), calculate the marginal utility of S and A.

Monotonic functions

Give an example to show that the intermediate value theorem becomes false if the hypothesis that f is continuous is replaced with f being montone, or with f being strictly monotone. (can use the same counterexample for both)

Topological limit of a function

Let X be a subset of R, let E be a subset of X, let x_0 be an adherent point of E, and let f: X-->R, g: X-->R, h: X-->R be functions such that f(x) <= g(x) <= h(x) for all x belonging to E. If we have lim of x-->x_0; x belonging to E of f(x) = lim of x-->x_0; x belonging to E of h(x) = L for some real number L, show that lim

Math: Drawing a scatter plot

Height Head circumference 27.25 17.4 25 17.2 26.75 17.3 25 17 28 17.6 26.25 17.2 25.75 17.1 27 17.3 If a Doctor wants to use height to predict head circumference which variable is the explanatory variable and which

Evaluate and graph the given functions.

1. Evaluate the function f(x) = 9x - 6 for x=0. 2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost? 3. Find the slope of the line through the poin

Find slope and interpret slope (rate of change)

In 1990, the minimum wage was about $3.50 per hour, and in 2005 it was 5.15. a) Find the slope of the line passing through the points (1990, 3.5) and (2005, 5.15). b) Interpret the slope as a rate of change. c) If this trend continues, estimate the minimum wage in 2015.

Application of Bolzano-Weierstrass Theorem

Recall that a point z0 is an accumulation point of a set S if each deleted neighborhood of z0 contains at least one point in S. ------------------------------------------------------------------------------------- One form of the Bolzano-Weierstrass theorem can be stated as follows: An infinite set of points lying in

Linear Programming Graphically

Solve the following linear programming problems graphically: Maximize profit = 4X + 6Y Subject to: X + 2Y ? 8 5X + 4Y ? 20 X,Y ? 0 Minimize cost = 24X + 15Y Subject to: 7X + 11Y ? 77 16X + 4Y ? 80

Statistical Concepts

Plotting the Binomial Probabilities using MINITAB 1.) Create plots for the three binomial distributions above. Select Graph > Scatter Plot and Simple then for graph 1 set Y equal to 'one fourth' and X to 'success' by clicking on the variable name and using the "select" button below the list of variables. Do this two more ti