Question

How do you find the domain and range of $y = 2x + 3$?

Answer 1

Hint: In this question, we have been asked to find the domain and range of $y = 2x + 3$. First, study what domain and range are. Then, look for the possible values of $x$. These possible values constitute our domain. The resultant values of $y$ that we get, after putting the various values of $x$ is our range.

Complete step-by-step solution:
We have to find the domain and range of $y = 2x + 3$. But first, let us find out the meaning of domain and range.
What is domain? In mathematics, the domain or set of departure of a function is the set into which all of the input of the function is constrained to fall. In simple words, domain is a set of all the possible values that can be put in the given equation or expression. These are the values of $x$.
What is range? Range is the set of all those values that a function takes when there is an input in the question. These are the values of $y$.
Now, let us move towards the question. First, we will find the domain.
What all can we put in the place of $x$? All the real numbers can take a place of $x$ as no number will give it an undefined value. Hence, the domain of the given equation is $\left( { - \infty ,\infty } \right)$.
Now, let us find the range. For this, I will plot the equation on the graph.

As we can see, for every value of $x$, there exists a certain value of $y$, and there is no break in the graph. Therefore, the range of the given function is $\left( { - \infty ,\infty } \right)$.

Hence the domain and range of the given linear equation is $\left( { - \infty ,\infty } \right)$.

Note: There is also another term called co-domain. What is co-domain? Co-domain is the possible values that could come out. Range is the subset of co-domain. The difference between the two is that range is the set of actual values that come out whereas co-domain is the set of possible values that “could” come out. In many cases, these two might be the same also.