if 2

if 2<x<3  and 3<y<4 ,then the range of  $${\frac{{\mathtt{x}}}{{\mathtt{y}}}}$$  is?

 

Well the highest value would be the biggest x over the smallest y :  3/3=1  (not inclusive)

and the lowsest value would be smallest x over the biggest y :  2/4=0.5      (not inclusive)

So the range would be  (0.5,1)

 

NOW lets look at it a different way.

$$\frac{x}{y}=k\qquad\mbox{where k is a constant}$$      

if 2<x<3  and 3<y<4

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I am going to graph this useing Desmos but I will need to change the letters used

y=a/b where  2<a<3  and 3<b<4

https://www.desmos.com/calculator/hap7do8n66

If you play with the sliders you will see the same result.  (It is the value of y)