00:01
Now before we could determine which among the given statement is false, we first want to define what is a domain and what is a range.
00:09
Now, domain of a function is the set of all valid values of the independent variable.
00:19
This independent variable is sometimes represented by x.
00:24
While the range is the set of all valid values of the dependent variable that is mostly represented by y.
00:34
Now the values of the domain and the range will depend on how we define our function.
00:44
So for the first statement when it says the domain and the range can have a similar set of values, this statement is true.
00:58
An example of that would be y equals x for x in the real number line.
01:09
So since x and y are the same, then the values of the domain and the range will be the same as well.
01:20
Now for the second statement which says the range of some functions is strictly positive, this is also true.
01:27
An example of this would be the function, y equals 1 over the square root of x.
01:36
Because if you look at the graph of this function, it will be this graph.
01:41
In which you can see that as x gets smaller, the value of y approaches positive infinity, but as x gets smaller or as x gets larger, the value of y approaches zero...