Question

Does the equation x^2+7y^2=1 define y as a function of x?

Answer 1

\[y = 1/7(\sqrt{1-x ^{2}})\]

Answer 2

Thank you!!! Your awsome! I was not sure if I was soing the problem right or not! =)

Answer 3

Solving for y we get:\[y = \pm \sqrt{\frac{1-x^2}{7}}\]If we take both values for the square root, it's not a function, because of the vertical line test. If we choose either the positive square root or the negative square root, we get a function. As the question does not state either, it's not.

Answer 4

thank you, execlent work! That was my first question and Im very impressed at how fast that was!

Answer 5

Notice, this is the negative square root graph: http://www3.wolframalpha.com/Calculate/MSP/MSP2071a167050hh0cdhge0000591e067h3939c5ab?MSPStoreType=image/gif&s=47&w=320&h=127&cdf=RangeControl
This is the positive: http://www3.wolframalpha.com/Calculate/MSP/MSP15091a166hgidedee05c00001c21h1bf4g2g6b0f?MSPStoreType=image/gif&s=44&w=319&h=136&cdf=RangeControl

If we pick both, notice how we are left with an ellipsis. That's not a function y(x).

Answer 6

The visual graphs are great! Thank you sooo much!
I am having such a hard time in my collage algebra right now. I've done great in everything but this!