Graphing in Algebra 1

Question

If the domain of f(x)=-x²  is integer values of x such that -3<(or equal to) x < 0, find the range.

Answer 1

Domain is the set of x values in which a function is defined.  Range is the set of y values in which a function is defined.  If a certain x value is not in the domain, then the function cannot be evaluated at the x value, because is it not defined there.

 

 

f(x) = -x²

 

Domain is in the interval  [-3, 0).

 

 

Evaluate f(-3) and f(0). 

 

f(-3) = -(-3)²

        = -(-3)(-3)

        = -9

 

f(0) = 0

 

 

Range is in the interval  [-9, 0)

 

Because x=-3 is included in the domain, f(-3) is included in the range.  That is why there are brackets in the starting points of domain and range. These are defined points.

 

The ending points of the domain and range are actually limits.  When x gets closer to 0, f(x) gets closer to 0.  That is why there are parentheses.