/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 9 How do you obtain the graph of \... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 9

How do you obtain the graph of \(y=f(3 x)\) from the graph of \(y=f(x) ?\)

Short Answer

Expert verified
\) Answer: The transformation \(y=f(3x)\) causes a horizontal compression of the graph of \(y=f(x)\) by a factor of 1/3.

Step by step solution

01

Identify the function transformation

Since we are given the transformation \(y=f(3x)\) from the initial function \(y=f(x),\) this transformation represents a horizontal compression of the graph by a factor of 1/3.
02

Determine the effect on the original graph

The horizontal compression by a factor of 1/3 will cause the x-values of the original points to shrink by 1/3, effectively compressing the graph horizontally. To do this, each original x-value, denoted by \(x_{original},\) will be transformed to a new x-value \(x_{new},\) using the relation \(x_{new} = \frac{1}{3}x_{original}.\)
03

Transform the original points

Now, we will transform each point on the graph of \(y=f(x)\) by compressing its x-coordinate value using the relation from Step 2: \(x_{new} = \frac{1}{3}x_{original}.\) Keep the y-coordinates the same. Apply this transformation to all major points on the graph, such as maximum or minimum values, intercepts, and any other significant points.
04

Draw the graph of \(y=f(3x)\)

Once you have transformed all the important points on the graph of \(y=f(x),\) connect the new points to recreate the graph of the transformed function, \(y=f(3x).\) Ensure that the shape of the graph is preserved and that it resembles a horizontally compressed version of the original graph. By following these steps, you can obtain the graph of \(y=f(3x)\) from the graph of \(y=f(x).\)

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