Question

In 2005, the shabelle river in Somalia rose an estimated 5.25 inches every hour for 15 hours. The increase in water level is represented by the function f(x)=5.25x, where x is the number of hours. Graph this function and give it's domain and range. Is the function discrete or continuous?

Answer 1

The Given situation is In 2005, the shabelle river in Somalia rose an estimated 5.25 inches every hour for 15 hours.

Increase in water level is represented by the function,f(x)=5.25 x.

or replacing f(x) by y we get ,y= 5.25 x

This is equation of straight line passing through the origin.

As x is number of hours , so x> 0,(0,∞] Which is it's domain.

As x> 0, so Range is those values of y for which x is defined.

`x= (y)/(5.25)`,So Range is y>0 i.e (0,∞}

As the function has no breaking point , that is when you plot the graph on coordinate axis there is no breaking point.So , it is everywhere continuous i. e for all values of x.