Question 128504
# 1


a)





Looking at {{{y=3x-4}}}, we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.


Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.



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 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)]








Now to find the range, simply graph the function to get





{{{graph(500,500,-10,10,-10,10,3x-4)}}}





From the graph, we can see that the function's y-values extend forever in both directions. So the range is also 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)]




<hr>



b)






Looking at {{{y=(x+9)/7}}}, we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.


Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.



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 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)]








Now to find the range, simply graph the function to get





{{{graph(500,500,-20,20,-20,20,(x+9)/7)}}}






From the graph, we can see that the function's y-values extend forever in both directions. So the range is also 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)]





<hr>



c)






Looking at {{{y=x^3+5}}}, we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.


Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.



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 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)]








Now to find the range, simply graph the function to get





{{{graph(500,500,-10,10,-10,10,x^3+5)}}}





From the graph, we can see that the function's y-values extend forever in both directions. So the range is also 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)]