2.9

//2.9
//The width of interval: half the difference of the lower and upper bounds 
//The width of the result combining two intervals is a function only of the widths of the argument intervals 
//Show that the width of the sum of 2 intervals is a function only of the widths of the intervals being added

//add two intervals 
//get the width of combined intervals 
//demonstrate that the width of the indivdual intervals effects the combined result of the combined interval 



function upper_bound(interval){
  return Math.max(interval);
}

function lower_bound(interval){
  return Math.min(interval);
}

function width_interval(x) {
    return (upper_bound(x) - lower_bound(x)) * .5;
}

function add_interval(x,y) {
   return make_interval(lower_bound(x) + lower_bound(y),
                        upper_bound(x) + upper_bound(y));
}

function sub_interval(x,y) {
   return make_interval(lower_bound(x) - upper_bound(y),
                        lower_bound(x) - upper_bound(y));
}


function make_interval(a,b) {
   return pair(a,b);
}

width_interval(add_interval(make_interval(1,2),make_interval(3,5)));
width_interval(sub_interval(make_interval(1,2),make_interval(3,5)));