Answered: given f(x) = x5 a) Determine a mapping…

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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Question

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 $f (a x)$ will compress the graph of $f (x)$ along the x-axis by a units.
The transformation of $f (x)$ to $a f (x)$ 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.