Circle Function Domain And Range

We now look at some examples of circles.

Circle function domain and range. Figure 2 range of values of trig functions. Therefore the domain of the sine and cosine is the set of real values r. Since the circle is a unit circle for any angle both sine and cosine are within the range of minus one to plus one. Hence y or y is a function.

The domain of y sin x is all values of x since there are no restrictions on the values for x. R x r range. In this article we will learn what a domain and range of a function mean and how to calculate the two quantities. 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.

Circles after all are finite and thus have finite domains and ranges. Assume the center is h k and the radius is r. X 2 y 2 25 centre 0 0 r 5. Therefore the range of each of these functions is a set of real numbers z such that 1 z 1 see figure 2.

R x r range. It depends on two things the radius and the center. The range of a circle is the y coordinate of the center of the circle plus and minus the radius of the circle. The points of the circle belong to set r.

Consequently the range of sine and cosine is the interval of 1. Here s how you can test the circles and semi circle functions. 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. Is a semi circle a function.

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. R y 0 for bottom semi circle. The range is more restricted. The domain of a circle is the x coordinate of the center of the circle plus and minus the radius of the circle.

It is easy to remember which coordinates domain and range refer to because x is alphabetically before y and domain is. Michael j s answer is a good graphical demonstration of how the symmetry of a circle yields domains and ranges of equal span. Before getting into the topic of domain and range let s briefly describe what a function is. Y 5 y 5 ii x 2 2 y 3 2 25 5 2 centre 2 3 r 5.

State the domain and range for each of the following functions and sketch its graph. Put any number into the sin function in your calculator. X 5 x 5 range. The domain and range of any real function is within the set of real numbers but we should narrow it down a bit.