given f(x) = x5 a) Determine a mapping rule that can be applied to f(x) = x5 to obtain the transformed function of y=3f (-1/2x - 1) + 4 b) Determine the image point of f(1) on the transformed graph. Show all your work

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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given f(x) = x5

a) Determine a mapping rule that can be applied to f(x) = x5 to obtain the transformed function of y=3f (-1/2x - 1) + 4

b) Determine the image point of f(1) on the transformed graph. Show all your work

Expert Solution
Step 1

Transformations of a function follow the following rules:-

  • The transformation of f(x) to f(x+a) will result in the shifting of the graph of f(x) to the left by a units.
  • The transformation of f(x) to f(ax) will compress the graph of f(x) along the x-axis by a units.
  • The transformation of f(x) to af(x) will stretch the graph of f(x) along the y-axis by a units.
  • The transformation of f(x) to f(x)+a will result in the shift of the graph of f(x) upwards by a units.
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