# Write the equation of a function with domain and range given, how to do that?

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The domain is #{-5<= x <= 5}#

The range is #{0<= y <= 5}#

How to do I determine the equation with these two things given?

The domain is

The range is

How to do I determine the equation with these two things given?

##### 1 Answer

#### Explanation:

One method is to construct a semicircle of radius

The equation for a circle centered at

Substituting in

Taking the principal root of both sides gives

graph{sqrt(25-x^2) [-10.29, 9.71, -2.84, 7.16]}

Note that the above only has a domain of

By the same token, however, we can simply define a function with the restricted domain

For example, we can define

If we are allowed to restrict our domain, then with a little manipulation, we can construct polynomials of degree