/*! 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 115 Begin by graphing the cube root ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 115

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
The graph of the cube root function \(f(x)= \sqrt[3]{x}\) is transformed by reflecting it in the x-axis and shifting 2 units to the left to obtain the graph of the function \(h(x)= -\sqrt[3]{x+2}\).

Step by step solution

01

Draw the graph for the cube root function

On a graph, plot the cube root function \(f(x)= \sqrt[3]{x}\). It will be a curve rising slowly, passing through points (1,1), (0,0), and (-1,-1).
02

Understand the transformation

The function \(h(x)= -\sqrt[3]{x+2}\) can be seen as the transformed function of \(f(x)\) where the function is shifted 2 units to the left and reflected in the x-axis to get the negative value.
03

Apply the transformation and plot the graph

To graph \(h(x)= -\sqrt[3]{x+2}\), reflect the graph of \(f(x)\) in the x-axis and then shift it 2 units to the left. You will get a curve falling slowly, passing through points (-1,-1), (-2,0), and (-3,1).

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

Solve for \(y: \quad A x+B y=C y+D\) (Section \(1.3, \text { Example } 8)\)

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$f(x)=\sqrt{x}, g(x)=x-1$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I have two functions. Function \(f\) models total world population \(x\) years after 2000 and function \(g\) models population of the world's more-developed regions \(x\) years after \(2000 .\) I can use \(f-g\) to determine the population of the world's less-developed regions for the years in both function's domains.

Find a. \((f \circ g)(x)\) b. the domain of \(f \circ g\) $$f(x)=x^{2}+1, g(x)=\sqrt{2-x}$$

Use a graphing utility to graph each circle whose equation is given. Use a square setting for the viewing window. $$x^{2}+y^{2}=25$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.