SOLUTION: How do we find the domain, range and intercepts of any given graph? For example, find the domain, range and intercepts of the graph of f(x) = x^2 + x - 1? NOTE: USE THE GR

(1)  The domain of this function is the set of all real numbers.

     In other words, the domain is the entire number line, from -infinity to +infinity.


     Thus question (1) is complete.



(2)  This function represents a parabola,

     Since the coefficient at x^2 is positive (it is 1 (one)), the parabola has the minimum.


     The range of this function is the set of its values, and it is the set of all real numbers 
     from the minimum of the parabola to infinity.

       
     So, to determine the range, we need to determine the minimum.


     The minimum of any quadratic function y = ax^2 + bx + c with positive coefficient "a" is at

          = .


     In our case it is   =  =  = -0.5.


     The minimum is   =  = 0.25 - 0.5 - 1 = -1.25.


     Therefore, the range of this quadratic function is from -1.25 to infinity.

     In the interval form, the range is  [-1.25,).


     Thus question (2) is complete.



(3)  To find x-intercepts, you need to solve this equation

         x^2 + x - 1 = 0.


     Use the quadratic formula

          =  = .


     The roots are   = =  0.618033989   (approximate),

               and   = = -1.618033989   (approximate).