Domain And Range Of A Circle Function

Michael j s answer is a good graphical demonstration of how the symmetry of a circle yields domains and ranges of equal span.

Domain and range of a circle function. The domain of a function is the collection of independent variables of x and the range is the collection of dependent variables of y. The range is more restricted. Y 5 y 5 ii x 2 2 y 3 2 25 5 2 centre 2 3 r 5. To find the domain of a function just plug the x values into the quadratic formula to get the y output.

The domain is the set of all values that can be input into a function and the respective output values are the. State the domain and range for each of the following functions and sketch its graph. The domain and range of any real function is within the set of real numbers but we should narrow it down a bit. The range of a circle is the y coordinate of the center of the circle plus and minus the radius of the circle.

Therefore the range of each of these functions is a set of real numbers z such that 1 z 1 see figure 2. The cosine and sine are the abscissa and ordinate of a point that moves around the unit circle and they vary between 1 and 1. Assume the center is h k and the radius is r. The domain is x l h r x h r the range is y l k r y k r for example if the center is 2 3 and the radius is 5 then the domain is from 3 to.

Put any number into the sin function in your calculator. Figure 2 range of values of trig functions. X 2 y 2 25 centre 0 0 r 5. The domain of a circle is the x coordinate of the center of the circle plus and minus the radius of the circle.

Any number should work and will give you a final answer between 1 and 1 from the calculator experiment and from observing the curve we can see the range is y betweeen 1 and 1 we could write this as 1 y 1. It is easy to remember which coordinates domain and range refer to because x is alphabetically before y and domain is. Circles after all are finite and thus have finite domains and ranges. Understand the domain and range of a function.

To find the range of a function first find the x value and y value of the vertex using the formula x b 2a. Here s how you can test the circles and semi circle functions.