Determine whether the equation determines y as a function of x and show all work

Algebra
Tutor: None Selected Time limit: 1 Day

Determine whether the equation determines y as a function of x and show work.

1.) 7x+1=y^3

2.) 3y-xy=x^2

Oct 3rd, 2015

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1.

7x+1=y^3

Step 1 Solve for y

Well we must take the third root of both sides.

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Since we do not get a unique y (because of the positive/negative), this is not a y as a function of x. (to be a function, it has to be one to one).

2.

3x-xy=x^2

Solve for y

pull out an x on the left side

x(3-y)=x^2 (divide both sides by x)

3-y=x (subtract three from both sides)

-y=x-3  (divide by -1 to both sides)

y=-x+3

Since we do get a unique y (because for every number, it will be a different kind of y), this is a y as a function of x. (since it is in fact one to one).


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 15th, 2015

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Oct 3rd, 2015
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Oct 3rd, 2015
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