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In point/list form, describe the transformations that were applied to create the function g(x) = -(3(x+2))* - 1

In point/list form, describe the transformations that were applied to create the function g(x) = -(3(x+2))* - 1

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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In point/list form, describe the transformations that were applied to create the function g(x) = −¹(3(x + 2))* — - 1 Create a rough sketch of a polynomial function that satisfies the following criteria: • degree 3 positive leading coefficient ● two zeros ● 2 turning points A polynomial function has the equation f(x) = 3x¹4 - 2x7 +5x² − x + 4. List three key characteristics of this function.
Transcribed Image Text:In point/list form, describe the transformations that were applied to create the function g(x) = −¹(3(x + 2))* — - 1 Create a rough sketch of a polynomial function that satisfies the following criteria: • degree 3 positive leading coefficient ● two zeros ● 2 turning points A polynomial function has the equation f(x) = 3x¹4 - 2x7 +5x² − x + 4. List three key characteristics of this function.
7. If y = x³ passes through the points (-1, -1), (0, 0) and (2,8), list the coordinates of these transformed points on the new curve if the following transformations have occurred. X 8. Determine the value of "a" f(x) is a quartic polynomial. 2nd difference -2 -1 0 a. Vertically compressed by a factor of 2 b. Reflected in the x-axis 1 2 3 c. Horizontally compressed by a factor of 0.5 d. Translated to the left 3 units and up 4 units y a 19 1st difference 61 10 3rd difference 12 4th difference 24 9. The function f(x) = x³ was transformed through a series of transformations. The resulting function g(x) was then transformed again by vertically compressing it by a factor of, horizontally stretching it by a factor of, horizontally translating it 5 units left, and vertically translating it 8 units down. The equation of the final function is h(x) = /[2(x + 1)]³ – 3. What was the equation of g(x)? Show your work or provide a detailed explanation for your solution
Transcribed Image Text:7. If y = x³ passes through the points (-1, -1), (0, 0) and (2,8), list the coordinates of these transformed points on the new curve if the following transformations have occurred. X 8. Determine the value of "a" f(x) is a quartic polynomial. 2nd difference -2 -1 0 a. Vertically compressed by a factor of 2 b. Reflected in the x-axis 1 2 3 c. Horizontally compressed by a factor of 0.5 d. Translated to the left 3 units and up 4 units y a 19 1st difference 61 10 3rd difference 12 4th difference 24 9. The function f(x) = x³ was transformed through a series of transformations. The resulting function g(x) was then transformed again by vertically compressing it by a factor of, horizontally stretching it by a factor of, horizontally translating it 5 units left, and vertically translating it 8 units down. The equation of the final function is h(x) = /[2(x + 1)]³ – 3. What was the equation of g(x)? Show your work or provide a detailed explanation for your solution
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