/*! 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 117 Begin by graphing the cube root ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 117

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 \(g(x) = \sqrt[3]{-x-2}\) is the graph of \(f(x) = \sqrt[3]{x}\) that's been flipped horizontally and shifted two units to the right.

Step by step solution

01

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

Plot the cube root function by choosing a variety of x-values, finding their cube roots, and then plotting the coordinates on a graph. Cube roots of negative numbers are negative and those of positive numbers are positive. So, the graph will go through the points (-1,-1), (0,0), and (1,1), giving a curve that increases slowly, crossing the x and y axes at the origin.
02

Understand The Transformation

The function \(g(x)=\sqrt[3]{-x-2}\) is the base cube root function but flipped horizontally (because of the negative sign before x) and shifted 2 units to the right (because of -2 inside the cube root).
03

Apply The Transformation and Graph

Flip the graph of \(f(x) = \sqrt[3]{x}\) over the y-axis to account for the negative sign before x. Then, shift the flipped graph 2 units to the right to account for the -2 inside the cube root to get the graph for \(g(x)\). It helps to take some positive and negative x values, evaluate their function values and plot these points to ensure accuracy.

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. $$x^{2}+y^{2}+8 x-2 y-8=0$$

Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(x\) -axis?

Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$\begin{aligned}(x-3)^{2}+(y+1)^{2} &=9 \\\y &=x-1\end{aligned}$$

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\sqrt{x-1}$$

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

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.