/*! 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

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: 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
To graph the function \(g(x)=\sqrt[3]{x}+2\), take the graph of the cube root function \(f(x) = \sqrt[3]{x}\), and shift it upwards by 2 units. Each point (x,y) on \(f(x)\) will transform to (x,y+2) on \(g(x)\).

Step by step solution

01

Graphing the cube root function

To graph the function \(f(x) = \sqrt[3]{x}\) consider various values of x. The cubic function's graph starts from negative infinity, crosses the origin (0,0) and goes to positive infinity. It is symmetric with respect to the origin.
02

Understanding the transformation

The given function \(g(x)=\sqrt[3]{x}+2\), differs from \(f(x)=\sqrt[3]{x}\) by the term +2. This represents a vertical shift of the graph upwards by 2 units. In graph transformation, adding a constant to the function results in the graph shifting vertically by that amount.
03

Applying the transformation

To graph \(g(x)=\sqrt[3]{x}+2\), start with the graph of \(f(x)=\sqrt[3]{x}\), and shift every point 2 units upwards. This means, each point \((x, y)\) on the graph of \(f\), will now be represented as \((x, y+2)\) on the graph of \(g\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x-2 y-8=0$$

Explaining the Concepts: If a function is defined by an equation, explain how to find its domain.

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-4 x-12 y-9=0$$

Will help you prepare for the material covered in the next section. $$\text { If }\left(x_{1}, y_{1}\right)=(-3,1) \text { and }\left(x_{2}, y_{2}\right)=(-2,4), \text { find } \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+8 x+4 y+16=0$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.