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?

1 Answer
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 [-8, 8]

By similar reasoning, the range is [-5, 5]

(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 = [-10, 10] and
Range = [-2, 2]

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 [-8, 2]

Now what about the range?

.

.

I hope you got Range is [0, 4], because that is correct.