Question

What is the domain and range of $y={{2}^{x}}$?

Answer 1

To solve this question first we will find all possible values of x will be possible. Then all possible values of x i.e. the possible set of inputs is known as the domain of the function and all corresponding values of y i.e. the possible outputs are known as the range of the given function.

Complete step by step answer:
We have been given a function $y={{2}^{x}}$.
We have to find the domain and range of the given function.
Now, when we observe the given function we get that for all values of x the given function gives the real values. There is no such value of x for which the given function is undefined.
So the domain of the given function is $\Rightarrow x\in R,\left( -\infty ,\infty \right)$
To find the range of the given function let us draw a graph of $y={{2}^{x}}$. Then we will get

When we observe the above graph we will find that the function is not continue at $y=0$ so the range of the given function will be
$\Rightarrow y > 0$
Hence above is the required domain and range of the given function.

Note: To solve such types of questions, a graphical method is most suitable. By plotting the graph of the given function we can check the point of discontinuity of the function. The point to be remembered is that the domain and range of a linear function is all real numbers.