/*! 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 110 Begin by graphing the cube root ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 110

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 graph of the function \(g(x) = \sqrt[3]{x - 2}\) can be obtained by taking the graph of the function \(f(x) = \sqrt[3]{x}\), and shifting it 2 units to the right. This means the function \(g(x)\) will be undefined for values of x less than 2, and will cross the x-axis at (2,0).

Step by step solution

01

Graph the Cube Root Function, \(f(x) = \sqrt[3]{x}\)

Begin by sketching the cube root function \(f(x) = \sqrt[3]{x}\). This function rises slowly, crosses the origin at (0,0), and continues to rise in the positive direction. The function is undefined for negative values of x.
02

Understand the Transformation

Looking at the transformed function \(g(x) = \sqrt[3]{x - 2}\), it is evident that every \(x\) in the original function \(f(x) = \sqrt[3]{x}\) has been replaced by \((x - 2)\). This represents a horizontal translation (or shift) of 2 units to the right.
03

Produce the Graph of the Transformed Function

Draw the graph of function \(g(x) = \sqrt[3]{x - 2}\) by shifting the graph of function \(f(x) = \sqrt[3]{x}\) two units to the right. This means, every point \((x, y)\) on the graph of function \(f(x)\) will move to the point \((x+2, y)\) on the graph of function \(g(x)\). So, instead of crossing the origin, the graph now crosses through (2,0)

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

A tangent line to a circle is a line that intersects the circle at exactly one point. The tangent line is perpendicular to the radius of the circle at this point of contact. Write an equation in point-slope form for the line tangent to the circle whose equation is \(x^{2}+y^{2}=25\) at the point (3,-4).

Will help you prepare for the material covered in the next section. Find the ordered pairs \((\quad, 0)\) and \((0, \quad)\) satisfying \(4 x-3 y-6=0\).

Will help you prepare for the material covered in the next section. -Consider the function defined by $$\\{(-2,4),(-1,1),(1,1),(2,4)\\}$$ Reverse the components of each ordered pair and write the eresulting relation. Is this relation a function?

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+x+y-\frac{1}{2}=0$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}-2 x+y^{2}-15=0$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Logic and Functions

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.