/*! 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 35 The graph of the function \(f\) ... [FREE SOLUTION] | 91影视

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Chapter 0: Problem 35

The graph of the function \(f\) is to be transformed as described. Find the function for the transformed graph. \(f(x)=\frac{\sqrt{x}}{x^{2}+1} ;\) stretched vertically by a factor of 3

Short Answer

Expert verified
The function for the transformed graph after stretching it vertically by a factor of 3 is: \(g(x) = \frac{3\sqrt{x}}{x^2 + 1}\).

Step by step solution

01

Recall the vertical stretching rule

: When a graph is vertically stretched by a factor of k, the transformation can be represented by the following rule: If \(g(x) = kf(x)\), then the graph of g(x) is the vertical stretch of the graph of f(x) by a factor of k.
02

Apply the vertical stretching rule to the given function

: We need to find a new function, g(x), that represents the vertical stretching of f(x) by a factor of 3. Using the rule from Step 1, we have: g(x) = 3f(x).
03

Replace f(x) with the given function and simplify

: We know that \(f(x) = \frac{\sqrt{x}}{x^2 + 1}\). Substitute this into the equation for g(x): g(x) = 3 * \(\frac{\sqrt{x}}{x^2 + 1}\). Now, simplify the expression by distributing the 3: g(x) = \(\frac{3\sqrt{x}}{x^2 + 1}\).
04

State the function representing the transformed graph

: The function for the transformed graph after stretching it vertically by a factor of 3 is: g(x) = \(\frac{3\sqrt{x}}{x^2 + 1}\).

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Most popular questions from this chapter

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