Question

How do you find the domain and range of $y=2x-1$ ?

Answer 1

These types of problems are pretty straight forward and are very simple to solve. This problem is a combination of algebra and functions which are used to determine the domain and range of various functions. The approach of solving this problem is to first find what all the different values can be of $x$ and then to find the possible values corresponding to $y$ . Hence all the possible values corresponding to $x$ is known as the domain and that corresponding to $y$ is known as the range of the given function $y$ .

Complete step-by-step solution:
Thus starting off with the given problem, we first try to find all the possible values of $x$ . Observing the equation carefully, we can safely say that there is no such value of $x$ which cannot be put in the equation for which the value of $y$ will be undefined. Thus we can conclude from our analysis that the domain of the function is $\left( -\infty ,\infty \right)$ , which means, we can put any real value of $x$ in the equation given to us. We can also write, $x\in R$ .
Now, we analyse the range of the given function. We can see that for any value of $x$, $y$ is always defined. We can have any real values of $y$ for any real $x$ . Thus we can very safely say that we can have any values of $y$ defined from $\left( -\infty ,\infty \right)$ . In other words we can say that the value of $y$ can be any real number. $y\in R$ .

Note: These types of problems can also be done by another method, which is basically the graphical method. In this method, we plot the function $y=2x-1$ , and check for any points of discontinuity. From the graph we can clearly observe that the graph goes on from a $\left( -\infty ,\infty \right)$ . This clearly explains that the domain of the function is $x\in R$ and the range of the function is $y\in R$.