Question 148198
When you graph {{{h(x)=2-sqrt(x-1)}}}, you get


{{{ drawing(500, 500, -10, 10, -10, 10,
 graph( 500, 500, -10, 10, -10, 10,2-sqrt(x-1))

)}}}



From the graph, we can see that the highest point is at (1,2). So this means that the highest y value is {{{y=2}}}. So this means that y can be any number less than or equal to 2. So this tells us that the range is {{{y<=2}}}



So the range in set-builder notation is  *[Tex \LARGE \left\{y\|y\le2\right\}]



Also the range in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-\infty,2}]<font size="8">]</font>