/*! 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 116 Begin by graphing the cube root ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 116

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

Short Answer

Expert verified
To graph \(h(x) = -\sqrt[3]{x - 2}\), shift the graph of the cube root function \(\sqrt[3]{x}\) 2 units to the right and then reflect it over the x-axis.

Step by step solution

01

Graph \(f(x) = \sqrt[3]{x}\)

To begin with, it's necessary to understand the basic graph of a cube root function. This function gets steeper for positive x and shallower for negative x. It passes through the origin (0,0).
02

Identify the Transformations

The function to be graphed, \(h(x) = -\sqrt[3]{x-2}\), is a transformation of the cube root function. \$h(x)\$ is obtained by shifting \(f(x)\) to the right by two units, and then reflecting it across the x-axis.
03

Apply the Horizontal Translation

The term inside the cube root function, \(x - 2\), is causing a shift to the right by 2. Each point on the graph of \(f(x)\) should be moved 2 units to the right.
04

Apply the Reflection

The negative sign in front of the cube root function causes a reflection of the graph across the x-axis. Each point on the graph should be reflected across the x-axis.
05

Graph the Transformed Function

After applying the shift and reflection, plot the transformed points to get the graph of \(h(x) = -\sqrt[3]{x-2}\). The graph will have the same shape as the original cube root function, but shifted and reflected.

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

determine whether each statement makes sense or does not make sense, and explain your reasoning. Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25 \quad\) and \((x-2)^{2}+(y+3)^{2}=36\)

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

determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding \(h\) and \(k,\) I place parentheses around the numbers that follow the subtraction signs in a circle's equation.

For people filing a single return, federal income tax is a function of adjusted gross income because for each value of adjusted gross income there is a specific tax to be paid. By contrast, the price of a house is not a function of the lot size on which the house sits because houses on same-sized lots can sell for many different prices. a. Describe an everyday situation between variables that is a function. b. Describe an everyday situation between variables that is not 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. $$ x^{2}-2 x+y^{2}-15=0 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete 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.