Question

How do you graph $y = 3\sqrt x $?

Answer 1

Hint: In order to determine the graph of the above equation, square on both sides of the equation, you will get a equation quadratic in variable $y$.So the graph will be a right ward opening parabola defined for positive y-axis . Draw some point from the equation and plot on the cartesian to get the accurate graph .

Complete step by step answer:
We are given an equation that is having two variables i.e. $y = 3\sqrt x $.Let’s find out the domain of the above equation, to know on what values of variable $x$the graph is going to be drawn.We can clearly see that the x cannot be negative .Therefore, equation is defined for all $x > 0$.
$x \in {\mathbb{Z}^ + }$
We cannot directly sketch the graph of the above equation. So we will be square on both sides of the equation. We get,
$
{\left( y \right)^2} = {\left( {3\sqrt x } \right)^2} \\
\Rightarrow{y^2} = 9x\,\,\, - - - - - (2) \\ $
As we know the equation of the form ${y^2} = 4ax$is a Rightward opening parabola having vertex at $(0,0)$. Since, from the equation (2) we can clearly see that the value of y is always positive.So the graph is not defined for the negative y-axis. Now we are going to graph, For that we are jumping on the cartesian plane.Lets find out some coordinates of points for equation (1)

X	0	4	9
y	0	6	9

Now plotting the rightward opening parabola for positive y-axis

Hence we’ve successfully plotted our graph of $y = 3\sqrt x $

Additional Information:
1.DOMAIN: Let R be a relation from a set A to a set B. Then the set of all first components or coordinates of the ordered pairs belonging to R is called the domain of R.Thus, domain of $R = \left\{ {a:(a,b) \in R} \right\}$
2.RANGE: Let R be a relation from a set A to a set B . Then the set of all second components or coordinates of the ordered pairs belonging to R is called as the range of R.Thus, Range of $R = \left\{ {b:\left( {a,b} \right) \in R} \right\}$

Note:1.A Cartesian Plane is given its name by the French mathematician Rene Descartes ,who first used this plane in the field of mathematics .It is defined as the two mutually perpendicular number line , the one which is horizontal is given name x-axis and the one which is vertical is known as y-axis. With the help of these axes we can plot any point on this cartesian plane with the help of an ordered pair of numbers.
2.Draw the cartesian plane only with the help of a straight ruler and pencil to get the perfect and accurate results.