Consider the exponential function
By definition, the domain of a function is the set of input argument values for which the function is real and defined.
Let we take then
then
then
If we chose larger values of x, we get larger function values.
For example, If we take
Thus if we choose smaller and smaller values of x. the f unction values will be smaller and smaller functions.
Thus the domain of the function is the set of all real numbers.
Thus the range is limited to the set of positive real numbers. That is,
If we choose larger values of x, we will get larger function values, as the function values will be larger powers of 2.
If we choose smaller and smaller x values, the function values will be smaller and smaller fractions.