Restrictions are very important when we talk about the domain and range of functions in Algebra II.
Domain Restrictions:
The domain is just all the possible values we can put in for x.
For example, in the function ( f(x) = \frac{1}{x-2} ), we can't use 2 as a value for x. So, the domain — or the set of possible x values — is ( (-\infty, 2) \cup (2, \infty) ). This means we can use any number except for 2.
Range Restrictions:
The range is all the possible results we can get out (y values).
Take ( g(x) = \sqrt{x} ) as an example. This function can only give us non-negative results, which means that y can be 0 or any positive number. So, the range for this function is ( [0, \infty) ).
When we understand these restrictions, we can better explain how functions work.
Restrictions are very important when we talk about the domain and range of functions in Algebra II.
Domain Restrictions:
The domain is just all the possible values we can put in for x.
For example, in the function ( f(x) = \frac{1}{x-2} ), we can't use 2 as a value for x. So, the domain — or the set of possible x values — is ( (-\infty, 2) \cup (2, \infty) ). This means we can use any number except for 2.
Range Restrictions:
The range is all the possible results we can get out (y values).
Take ( g(x) = \sqrt{x} ) as an example. This function can only give us non-negative results, which means that y can be 0 or any positive number. So, the range for this function is ( [0, \infty) ).
When we understand these restrictions, we can better explain how functions work.