# How would you find the domain and range of a circle on a graph whose points on the y axis are 5 and -5, and whose x axis coordinates are 8 and -8?

Mar 26, 2015

The curve you describe is not a circle, it could be an ellipse. Here is the curve I think you meant:

graph{x^2/64+y^2/25=1 [-20.27, 20.28, -10.14, 10.13]}

The domain is the set of all numbers for which there is a point on the curve with that $x$-value.
The range is the set of all numbers for which there is a point on the curve with that $y$-value.

It might be helpful to imagine squashing the graph down onto the $x$-axis to find the domain. The squashing it onto the $y$-axis to find the range.

For this graph, there are clearly no points with $x = - 20$ or $x = - 10$,
in fact the least number that appears as a, $x$-coordnate of a point on this graph is $- 8$. The greates is $8$ and there is a point on the curve for every number between $- 8$ and $8$. Therefore the Domain is $\left[- 8 , 8\right]$

By similar reasoning, the range is $\left[- 5 , 5\right]$

(Be careful to read the $y$-values from least to greatest -- from bottom to top.)

Here's another example:

Find the domain and range of the equation whose graph is:

graph{x^2/100+y^2/4=1 [-14.24, 14.25, -6.21, 8.03]}

I hope you got Domain = $\left[- 10 , 10\right]$ and
Range = $\left[- 2 , 2\right]$

One more example:

Find the domain and range of the equation whose graph is below.
Remember that the domain is all the $x$ values used and the range is the $y$-values used. You can zoom in if you use your mouse wheel.

graph{(x+3)^2/25+(y-2)^2/4=1 [-12.515, 9.995, -4.18, 7.07]}

It looks like we use all the $x$-values from $- 8$ to $2$

So the domain is $\left[- 8 , 2\right]$

Now what about the range?

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I hope you got Range is $\left[0 , 4\right]$, because that is correct.