CAN A FUNCTION HAVE AN INFINITE NUMBER OF VALUES IN ITS DOMAIN AND ONLY A FINITE NUMBER OV VALUES IN ITS RANGE

Question

Can a function have an infinite number of values in its domain and only a finite number in its range?

Answer 1

Hi Coco,

 

Yes, you could have a function like f(x) =2

 

the domain is all real numbers and the range is a single number

 

Hope this helps

Answer 2

The graph of a sine and cosine function is an example of a function that has infinite domain and finite domain. The range is finite because these graphs have an amplitude, which is the maximum or minimum value on the graph.  As for domain, the x-values are the pi-radians.  If we rotate the angle a full pi-radians and 2-pi radian an infinite amount of times from either direction, the sine and cosine graph will be continuous along the x-axis.

Answer 3

Yes.  As an example of such a function, let the domain be the interval

[0,1] on the x-axis and let the function have the value 0 at each of the rational points of that interval and 1 at each of the irrational points.