Question

What is the domain and range of a linear function?

Answer 1

Hint: Questions like these can be dealt very easily and solved quickly once we understand all the underlying concepts behind the problem. To solve it, we need to have a fair idea about functions and graphs. First off all we need to understand what the general equation of a linear function looks like. The general equation of a linear function is given by \[y=mx+c\] . Now analysing this function we need to find the domain and the range. We need to have a bit of experience about the nature of the functions in various conditions, for example, if we are given a linear function bounded by a particular interval, then the domain and range will be different in that case.

Complete step-by-step solution:
Now we start off with the solution to the given problem by writing that, the function \[y=mx+c\] , is increasing with an increase in ‘x’. There is no exception in the value of ‘x’ which may lead to an undefined value of ‘y’. So from this we can clearly say that the function is defined for all values of ‘x’. Thus the domain of the function is therefore \[\mathbb{R}\] . We have also seen that there is no undefined value of ‘y’ for all values of ‘x’, so the range of the function is thus also \[\mathbb{R}\] .

Note: For solving these types of problems, we need to be thorough with our knowledge of functions and graphs. We need to be careful in finding out all the possible values of ‘x’ for which the value of ‘y’ becomes undefined and it needs to be eliminated from the domain. This problem can also be solved by drawing the graph of the respective function and then observing the domain and range from it.