/*! 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 83 Determine whether the function i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 83

Determine whether the function is even, odd, or neither. Then describe the symmetry. $$ f(x)=x^{6}-2 x^{2}+3 $$

Short Answer

Expert verified
The function \(f(x)=x^{6}-2x^{2}+3\) is an even function and it is symmetric about the y-axis.

Step by step solution

01

Substitute x with -x

Replace \(x\) with \(-x\) in the function, which would change \(f(x)\) to \(f(-x)\), resulting the function to be \(f(-x)=(-x)^{6}-2(-x)^{2}+3\).
02

Simplify the function

After simplifying, the equation becomes \(f(-x)=x^{6}-2x^{2}+3\), which is the same as the original function \(f(x)=x^{6}-2x^{2}+3\).
03

Compare with the original function

Comparing \(f(-x)\) and \(f(x)\), we see that \(f(-x) = f(x)\), so the function is an even function.
04

Describe the Symmetry

Since the function is even, it is symmetric about the y-axis.

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 if the situation could be represented by a one-to-one function. If so, write a statement that describes the inverse function. The depth of the tide \(d\) at a beach in terms of the time \(t\) over a 24 -hour period

The joint variation model \(z=k x y\) can be described as " \(z\) varies jointly as \(x\) and \(y\)," or \(" z\) is_____ _____ to \(x\) and \(y.\) "

The linear model with the least sum of square differences is called the _____ _____ _____ line.

Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring. A force of 265 newtons stretches a spring 0.15 meter (see figure). (a) How far will a force of 90 newtons stretch the spring? (b) What force is required to stretch the spring 0.1 meter?

Determine if the situation could be represented by a one-to-one function. If so, write a statement that describes the inverse function. The population \(p\) of South Carolina in terms of the year \(t\) from 1960 through 2008
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.