Courses
Courses for Kids
Free study material
Offline Centres
More
Store

How do you graph $y = \sqrt {x + 4}$ ?

Last updated date: 11th Jun 2024
Total views: 372.6k
Views today: 3.72k
Verified
372.6k+ views
Hint:In order to determine the graph of the above equation, square on both sides of the equation, you will get an equation quadratic in variable $y$. So the graph will be a rightward opening parabola defined only for positive y-axis .Having the domain of the equation as $x \in \left[ { - 4,\infty } \right)$. Find out some good values of the equation by putting $x = - 3,0,5$ plot on the cartesian to get the accurate graph .

Complete step by step solution:
We are given a equation that is having two variables i.e.
$y = \sqrt {x + 4}$---(1)
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 $x + 4$ cannot be negative. Therefore, equation is defined for all $x + 4 \geqslant 0 \Rightarrow x \geqslant - 4$
$\therefore x \in \left[ { - 4,\infty } \right)$
We cannot directly sketch the graph of the above equation. So we will be square on both sides of the equation. We get,
${\left( y \right)^2} = {\left( {\sqrt {x + 4} } \right)^2} \\ {y^2} = x + 4\,\,\, - - - - - (2) \\$
Graph will be a rightward opening parabola as the equation is quadratic in $y$
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.
Let's find out some good values of $x\, and \,y$, in other words some coordinates of points for equation (1).

Hence we’ve successfully plotted our graph of $y = \sqrt {x + 4}$

Thus, domain of $R = \left\{ {a:(a,b) \in R} \right\}$
Thus, Range of $R = \left\{ {b:\left( {a,b} \right) \in R} \right\}$