Answered: use the following analysis steps to…

use the following analysis steps to make a graph of the function. fta) = 1. x and y intercepts 2. vertical and horizontal asymptotes 3. end behavior (use format presented in class) I-3

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.2: Domain And Range

Problem 61SE: The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is...

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Suppose you have a job that pays $8.50 per hour and you work anywhere from 10 to 40 hours per week. a. Write an equation, with a restriction on the variable x, that gives the amount of money, y, you will earn for working x hours in one week. b. Use the function rule you have written in part (a) to complete Table 4. c. Construct a line graph from the information in Table 4. d. State the domain and range of this function.
The ad shown at left was in the local newspaper. Suppose you are hired for the job described in the ad. a. If x is the number of hours you work per week and y is your weekly gross pay, write the equation for y. (Be sure to include any restrictions on the variable x.) b. Use the function rule you have written in part (a) to complete Table 5. c. Construct a line graph from the information in Table 5. d. State the domain and range of this function. e. What is the minimum amount you can earn in a week with this job? What is the maximum amount?
For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant. 31. Find the local extrema for the function graphed in Exercise 28.
In this problem you are asked to find a function that models in real life situation and then use the model to answer questions about the guidelines on page 273 to help you. Minimizing Time A man stands at a point A on the bank of a straight river, 2 mi wide. To reach point B, 7 mi downstream on the opposite bank, he first rows his boat to point Pon the opposite bank and then walks the remaining distances x to B, as shown in the figure. He can row at a speed or 2 mi/h and walk as a speed of mi/h (a) Find a function that models the time needed for the trip. (b) Where should he land so that he reaches B as soon as possible?
When Limiting Values Occur Suppose S(t) represents the average speed, in miles per hour, for a 100-mile trip that requires t hours. Explain why we expect S to have a limiting value.
The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?
For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. k(x)=6x^4+32x^3 a) What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The relative minimum point(s) is/are enter your response here and the relative maximum point(s) is/are enter your response here. (Simplify your answers. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) B. The relative maximum point(s) is/are enter your response here and there are no relative minimum point(s).…
Determine the smallest value of the constant a for which the graph of the function f(x) = ax−x is always above the x−axis. Help me fast so that I will give good rating.
The graph of y=f(x) to the right gives the speed limit y along a rural highway x miles from its starting point. (a) What are the maximum and minimum speed limits along this stretch of highway? Estimate the miles of highway with a speed limit of 50 miles per hour. (b) Evaluate f(16), f(32), and f(36). And at what x-values is the graph discontinuous? Interpret each discontinuity.a) Along this stretch of highway, the maximum speed limit is ___ miles per hour and the minimum speed limit is ____ miles per hour.There are ___ miles of highway with a speed limit of 50 miles per hour.b) Evaluate.f(16) = _____f(32) = _____f(36) = _____At what x-values is the graph discontinuous? _____ (Use a comma to seperate answers.)Interpret the discontinuities. Choose the correct interpretaion below.A) The speed limit changes at each discontinuity.B) The road changes names at each discontinuity.C) There is no speed limit data for the discontinuities.D) The altitude changes at each discontinuity.
VI, For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph.
Population growth in the U.S. between 1800 and 1850, in millions, can be represented by the function f defined by f (t)=5*e (0.028t). What was the U.S. population in 1800? Use graphing technology to graph the equations y=f(t) and y=20. Adjust the graphing window to the following boundaries: 0<x<100 and 0<y<40. What is the point of intersection of the two graphs, and what does it mean in this situation?
An icicle that is 12 mm long melts at a constant rate of 1.2 mm per minute. Let t represent the number of minutes since the icicle started melthing and suppose R is a function such that R(t) represents the remaining length of the icicle (in mm) t minutes after it started melting. A.What is the domain of R−1 relative to this context? Enter your answer as an interval. b.What is the range of R−1 relative to this context? Enter your answer as an interval. c.Solve R(t)=6.6 for t t= d.What does your solution in part (f) represent in this context? Select all that apply. How long it takes for the icicle to melt completely. How many minutes since the icicle started melting when it is 6.6 mm long. The length of the icicle (in mm) 6.6 minutes after it started melting.