Homework Help

Determine whether the equation defines y as a function of x. `7x^2+3y^2=1`

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mcelwee5 | Student, College Freshman | (Level 1) Honors

Posted August 20, 2012 at 3:47 PM via web

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Determine whether the equation defines y as a function of x.


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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted August 20, 2012 at 4:46 PM (Answer #1)

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First we will have to isolate y on the left side.

`==gt 7x^2 + 3y^2 = 1`

` ==gt 3y^2 = 1- 7x^2 `

`==gt y^2 = (1-7x^2)/3 `

`==gt y= +- (1-7x^2)/3`

`` Now we notice that we have two possible values to y for each value of x.

Therefore, we have two images for the value of x ( positive value and negative value.

For example, if x= 1 ==> y= 2 and y= -2)

Then, y is NOT a function of x.

Or, we can graph y and test the vertical line.

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Wiggin42 | Student, Undergraduate | TA | (Level 2) Valedictorian

Posted May 28, 2014 at 8:43 PM (Answer #2)

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Isolate y so we can find out if this is indeed a function or not: 

`3y^2 = 1 - 7x^2`

`y^2 = ( 1 - 7x^2 ) / 3`

`y = sqrt ( (1 - 7x^2) / 3 )`

` `

We know that the square root means both positive and negative. So when we plug this into a graphing utility, we need to account for both positive and negative. And when you do this, you'll see that the resulting image is that of a circle which does not pass the vertical line test and so is not a function. 

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