Question 128578
{{{drawing(500,500,-10,10,-10,10,
grid(1),
graph(500,500,-10,10,-10,10,x+1)
)}}}


Looking at the graph, notice how the line extends to infinity in all four directions. So this shows us that there are no restrictions on the domain.




Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in <b>any</b> in for x





So the domain of the function in set-builder notation is:



*[Tex \LARGE \textrm{\left{x|x\in\mathbb{R}\right}}]



In plain English, this reads: x is the set of all real numbers (In other words, x can be <b>any</b> number)



Also, in interval notation, the domain is:


*[Tex \Large \left(-\infty,\infty \right)]



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Also, since there are no restrictions on the range, this means that the range is all real numbers. 





So the range of the function in set-builder notation is:



*[Tex \LARGE \textrm{\left{y|y\in\mathbb{R}\right}}]



In plain English reads: y is the set of all real numbers (In other words, y can be <b>any</b> number)



Also, in interval notation, the range is:


*[Tex \Large \left(-\infty,\infty \right)]