/*! 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 107 Begin by graphing the cube root ... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 107

Begin by graphing the cube root function, \(f(x)=\sqrt[3]{x} .\) Then use transformations of this graph to graph the given function. $$g(x)=\sqrt[3]{x}+2$$

Short Answer

Expert verified
The function \(g(x) = \sqrt[3]{x} + 2 \) is a vertical shift of the cube root function, where the graph moves 2 units upwards on the y-axis.

Step by step solution

01

Graph the parent function

The parent function for this exercise is \(f(x)=\sqrt[3]{x}\). To graph this function, choose a set of x-values, calculate the corresponding y-values, and plot the points. For instance, when \(x = -8, -1, 0, 1, 8\), \(f(x) = -2, -1, 0, 1, 2\), respectively.
02

Apply the transformation

The given function, \(g(x)=\sqrt[3]{x} + 2\), is a vertical transformation of the parent function where all y-values are increased by 2. Calculate the new y-values by adding 2 to each of the corresponding y-values from the parent function. With \(x = -8, -1, 0, 1, 8\), \(g(x) = 0, 1, 2, 3, 4\), respectively.
03

Graph the transformed function

Plot these new set of points on the same coordinate system as the parent function to see the differences clearly. The curve of the graph will move upward by 2 units, thus displaying the transformation.

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