Concept explainers
For Exercises 1-14,
a. Write the domain.
b. Write the range.
c. Find the
d. Find the
e. Determine the asymptotes if applicable.
f. Determine the intervals over which the function is increasing.
g. Determine the intervals over which the function is decreasing.
h. Match the function with its graph.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Precalculs
Additional Math Textbook Solutions
Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (2nd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
- A company determines that its weekly profit from manufacturing and selling x units of a certain item is given by Px=-x3+3x2+2880x-500. Use a graphing utility to find the weekly production rate that will maximize the profit.arrow_forwardSuppose 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.arrow_forwardA business has a cost function of C=0.4x+8000, where C is measured in dollars and x is the number of units produced. The average cost per unit is given by C=Cx=0.4x+8000x,x0. a. Find the average costs per unit when x=1000,x=8000,x=20,000,andx=100,000. b. What is the horizontal asymptote of the graph of this function, and what does it represent?arrow_forward
- For the graph in Figure 3, the domain of the function is [3,3] . The range is [10,10] . Find the absolute minimum of the function on this interval.arrow_forwardSuppose the range of a function fis [5,8] . What is the range of |f(x)| ?arrow_forwardA company is planning to manufacture mountain bikes. The fixed monthly cost will be $100,000 and it will cost $100 to produce each bicycle. Solve; a. Write the cost function, C, of producing x mountain bikes. b. Write the average cost function, C*, of producing x mountain bikes. c. Find and interpret C*(500), C*(1000), C*(2000), and C*(4000). d. What is the horizontal asymptote for the graph of the average cost function, C*? Describe what this means in practical terms.arrow_forward
- The total revenue (TR in $) for a textbook on mathematical economics is given by the equation TR = 1800Q − Q2 − 44375, where Q is the number of books sold. a.Draw the graph of the TR function using the example as in WolframAlpha. Can you guess the number of books to be sold to maximise the revenue? (Please take a snip of your graph and add it to your document) b. Find the number of books sold when the TR is $765,625? You can apply the quadratic formula or the method of completing squares.arrow_forwardA T-shirt manufacturer is planning to expand its workforce. It estimates that the number of T-shirts produced by hiring x new workers is given by T(x)=−0.75x4+9x3, 0≤x≤9. When is the rate of change of T-shirt production increasing and when is it decreasing?( Type your answer in interval notation.) What is the point of diminishing returns and the maximum rate of change for T-shirt production? Graph T and T′ on the same coordinate system.arrow_forwardSuppose that a company has just purchased a new computer for $2400. The company chooses to depreciate using the straight-line method for 4 years? (a) Write a linear function that expresses the book value V of the computer as a function of its age x. (b) What is the domain of the function found in part (a)? (c) Graph the linear function. (d) What is the book value of the computer after 2 years? (e) When will the computer have a book value of $600?arrow_forward
- Student Loans Data for selected years from 2011and projected to 2023 can be used to show that thebalance of federal direct student loans y, in billions ofdollars, is related to the number of years after 2010,x, by the function y = 130.7x + 699.7.a. Graph the function for x-values corresponding2010 to 2025.b. Find the value of y when x is 13.c. What does this function predict the balance offederal direct student loans will be in 2029?(Source: U.S. Office of Management and Budget)arrow_forwardA2. Ms. Whitmell says that the odd degree function she's looking at has a domain of {x∈ℝ} and {y∈ℝ}. If she solves for the turning points of the function, will that change the values for the domain or range Question 1 options: Yes, it will affect the domain Yes, it will affect the range Yes, it will affect the domain and the range No, it will affect neither the domain nor the rangearrow_forwardAttached is the graph of the function g(x) = |x| What would the graph of kg(x) when -4 < k < -1 look like?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
- Trigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage