The graphs of four functions f, g, h, and i are shown below. + 4y 3-...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The graphs of four functions f, g, h, and i are shown below. + 4y 3- -2 1 1 2 3 + + x 5 6 Read carefully: The functions below must be written in terms of f, g, h, or i as indicated. If your answer only includes the letter x without one of the functions indicated, it will not be answering the question correctly. Although you may realize that f(x) = x, use the general name for this function and not the x. The point of this question is to understand how transformations work on general functions, not just on specific functions. This kind of remark is typically not included in questions as the question does explicitly tell you how to write your answer. The remark is added here to help you learn as it addresses a common mistake on the midterm. a. Write g(x) in terms of transformations of f. Then g(x) = b. Write f(x) in terms of transformations of g. Then f(x) = c. Write h(x) in terms of transformations of f. Then h(x) = Preview Preview Preview d. Write i(x) in terms of vertical transformations of f that can only occur at integer multiples of 0.5 (so 0.5, -0.5, 1, etc). i(x): = Preview The graph of a polynomial function f is shown below. + 4y 3 2 -3 -2 -1 2 +1 -2 + 8 Answer the following questions and use them to help write an equation for f. If there is more than one answer, separate your answers with a comma. Assume the coefficient on the leading term has absolute value of 0.25 and that f only has real roots. a. The root(s) of f with odd multiplicity is (are) b. The root(s) of with even multiplicity is (are) c. The coefficient on the leading term is Preview Preview Preview d. Assume roots with odd or even multiplicity have multiplicity 1 or 2, respectively. Write an equation for f. f(x) = Preview = 16t + 37t + 120 determines the height of the snowball A snowball is thrown upward from a bridge into a river below. The function f(t) above the surface of the water (in feet) in terms of the number of seconds t since the snowball was thrown. To help you answer questions c. and d., remember that a parabola is symmetric about the vertical line through the vertex (axis of symmetry) and so both zeros off are the same distance from the axis of symmetry. Depict the path off the snowball by hand (do not use an external tool/grapher). a. What is the bridge's height above the water? feet Preview b. How many seconds after being thrown does the snowball hit the water? seconds Preview c. How many seconds after being thrown does the snowball reach its maximum height above the water? seconds Preview d. What is the snowball's maximum height above the water? feet Preview The graph of a quadratic function f is shown below. 4y 3 2 x -4 -2 -1 3 4 N + Answer the following questions and use them to help write an equation for f. If there is more than one answer, separate your answers with a comma. a. The roots of are -3, 1 Preview b. The coordinates, (x, y), of the vertex of f is (-1,-2) c. The coefficient on x2 is: 1 d. Write an equation for f. f(x) = = (x+1)^2+2x-3 Preview Preview Preview The graphs of four functions f, g, h, and i are shown below. + 4y 3- -2 1 1 2 3 + + x 5 6 Read carefully: The functions below must be written in terms of f, g, h, or i as indicated. If your answer only includes the letter x without one of the functions indicated, it will not be answering the question correctly. Although you may realize that f(x) = x, use the general name for this function and not the x. The point of this question is to understand how transformations work on general functions, not just on specific functions. This kind of remark is typically not included in questions as the question does explicitly tell you how to write your answer. The remark is added here to help you learn as it addresses a common mistake on the midterm. a. Write g(x) in terms of transformations of f. Then g(x) = b. Write f(x) in terms of transformations of g. Then f(x) = c. Write h(x) in terms of transformations of f. Then h(x) = Preview Preview Preview d. Write i(x) in terms of vertical transformations of f that can only occur at integer multiples of 0.5 (so 0.5, -0.5, 1, etc). i(x): = Preview The graph of a polynomial function f is shown below. + 4y 3 2 -3 -2 -1 2 +1 -2 + 8 Answer the following questions and use them to help write an equation for f. If there is more than one answer, separate your answers with a comma. Assume the coefficient on the leading term has absolute value of 0.25 and that f only has real roots. a. The root(s) of f with odd multiplicity is (are) b. The root(s) of with even multiplicity is (are) c. The coefficient on the leading term is Preview Preview Preview d. Assume roots with odd or even multiplicity have multiplicity 1 or 2, respectively. Write an equation for f. f(x) = Preview = 16t + 37t + 120 determines the height of the snowball A snowball is thrown upward from a bridge into a river below. The function f(t) above the surface of the water (in feet) in terms of the number of seconds t since the snowball was thrown. To help you answer questions c. and d., remember that a parabola is symmetric about the vertical line through the vertex (axis of symmetry) and so both zeros off are the same distance from the axis of symmetry. Depict the path off the snowball by hand (do not use an external tool/grapher). a. What is the bridge's height above the water? feet Preview b. How many seconds after being thrown does the snowball hit the water? seconds Preview c. How many seconds after being thrown does the snowball reach its maximum height above the water? seconds Preview d. What is the snowball's maximum height above the water? feet Preview The graph of a quadratic function f is shown below. 4y 3 2 x -4 -2 -1 3 4 N + Answer the following questions and use them to help write an equation for f. If there is more than one answer, separate your answers with a comma. a. The roots of are -3, 1 Preview b. The coordinates, (x, y), of the vertex of f is (-1,-2) c. The coefficient on x2 is: 1 d. Write an equation for f. f(x) = = (x+1)^2+2x-3 Preview Preview Preview
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these mathematics questions
-
Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
At the beginning of compression in a diesel cycle, T = 540 R, P = 30 lbf/in. 2 , and the state after combustion (heat addition) is 2600 R and 1000 lbf/in. 2 . Find the compression ratio, the thermal...
-
$69 is 30% of what amount?
-
Magic Company adds materials at the beginning of the process in Department A. The following information on physical units for Department A for the month of August is available: Work in process,...
-
Why is the balanced scorecard methodology balanced?
-
The following financial information is for Frizell Company. Additional information: 1. Inventory at the beginning of 2013 was $115,000. 2. Accounts receivable (net) at the beginning of 2013 were...
-
Fall Clothes Line Promotion Market research and analysis show that the proposed advertising media for the new fall lines need to be reprioritized and changed. Findings from focus groups and surveys...
-
Describe corporate social irresponsibility. Where do you stand on the issue of CSR v CSI? Do corporations have a right to ignore their responsibility to some stakeholders in order to add to the short...
-
Granulosus Co. purchased 60 percent of the voting shares of Losillas Corp. on July 15, 2017, at that day's book value. On that date, the fair value of uncontrollable interest was equal to 35 per...
-
Due to competition, Durango is considering lowering the unit sales price by 12% next year and increasing fixed marketing expenses by $60,000. If these changes are made, how many units must be sold...
-
On October 1, 2022, Deebo Mfg. got a 12-month loan of $400,000, bearing interest at 10% per year. Interest is payable in full at maturity on September 30, 2023. In connection with this loan, how much...
-
If f(x) = (4x-5)4 (3x + 6), find f'(x) using logarithmic differentiation.
-
What is (f ) '(0)?
-
Prepare a power point presentation to explain the following. Over the past year, the management of U.S. Security Associates, Inc. have realize the significance of having an efficient team that is...
-
Prove the formula for (d/dx)(cos-1x) by the same method as for (d/dx)(sin-1x).
-
Fill in the Blank. __________ equation involves time-dependent coefficients.
-
Fill in the Blank. When finite amplitudes of motion are involved, __________ analysis becomes necessary.
-
Fill in the Blank. __________ principle is not applicable in nonlinear analysis.
Study smarter with the SolutionInn App