/*! 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 11 Determine whether the equation r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 11

Determine whether the equation represents \(y\) as a function of \(x .\) $$x^{2}+y^{2}=4$$

Short Answer

Expert verified
No, the equation does not represent \(y\) as a function of \(x\) because there are two possible values of \(y\) for each value of \(x\) in the domain.

Step by step solution

01

Rearrange equation

Rearrange the equation to isolate \(y\) in terms of \(x\), this is done by subtracting \(x^2\) on both sides of the equation: \(y^2 = 4 - x^2\)
02

Solving for y

In order to get \(y\) on one side, we take the square root of both sides, however, we have to take into account that the square root has two possible values, positive and negative. This leads us to the equation: \(y = \sqrt{4 - x^2}\) and \(y = -\sqrt{4 - x^2}\)
03

Function analysis

Since there are two possible values of \(y\) for each value of \(x\) in the domain where the square root is defined (\(-2 \leq x \leq 2\)), \(y\) is not a function of \(x\).

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

Finding a Mathematical Model In Exercises \(41-50\), find a mathematical model for the verbal statement. \(z\) varies jointly as the square of \(x\) and the cube of \(y\)

Find the difference quotient and simplify your Answer: $$f(x)=x^{3}+3 x, \quad \frac{f(x+h)-f(x)}{h}, \quad h \neq 0$$

The height \(y\) (in feet) of a baseball thrown by a child is $$y=-\frac{1}{10} x^{2}+3 x+6$$ where \(x\) is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to catch the ball? (Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)

The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 440 vibrations per second. Find the frequency of a string that has 1.25 times as much tension and is 1.2 times as long.

Find the difference quotient and simplify your Answer: $$f(x)=x^{2}-x+1, \quad \frac{f(2+h)-f(2)}{h}, \quad h \neq 0$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

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.