Question

How do you graph $y = 2 - \sqrt {x - 2} $ by plotting points?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of the graph is generally represented as $y = f\left( x \right)$, where $x$ and $f(x)$ are real numbers. We substitute the value of x and we determine the value of y and then we mark the points in the graph and we join the points.

Complete step by step solution:
Here in this question, we have to plot the graph for the given function. A graph of a function is a set of ordered pairs and it is represented as $y = f\left( x \right)$, where $x$ and $f(x)$ are real numbers. These pairs are in the form of Cartesian form and the graph is the two-dimensional graph.
First, we have to find the domain of the given function as it involves square root due to which we cannot substitute each and every real value of x.
So, the domain of the function $y = 2 - \sqrt {x - 2} $ should be the setoff values of x for which the term inside the square root $\left( {x - 2} \right)$ is non negative.
Hence, $\left( {x - 2} \right) \geqslant 0$
$ \Rightarrow x \geqslant 2$
So, we can only substitute the values of x that are greater than or equal to $2$.
So, let us substitute the value of x as \[2\], \[3\], $6$ and $11$.
Now we consider the value of x as \[2\], the value of y is
$ \Rightarrow y = 2 - \sqrt {2 - 2} $
$ \Rightarrow y = 2 - \sqrt 0 $
$ \Rightarrow y = 2$
Now we consider the value of x as \[3\], the value of y is
$ \Rightarrow y = 2 - \sqrt {3 - 2} $
$ \Rightarrow y = 2 - 1$
$ \Rightarrow y = 1$
Now we consider the value of x as $6$, the value of y is
$ \Rightarrow y = 2 - \sqrt {6 - 2} $
$ \Rightarrow y = 2 - \sqrt 4 $
$ \Rightarrow y = 2 - 2$
$ \Rightarrow y = 0$
Now we consider the value of x as $11$, the value of y is
$ \Rightarrow y = 2 - \sqrt {11 - 2} $
$ \Rightarrow y = 2 - \sqrt 9 $
$ \Rightarrow y = 2 - 3$
$ \Rightarrow y = - 1$
Now we draw a table for these values we have

x	$2$	\[3\]	\[6\]	\[11\]
y	$2$	\[1\]	\[0\]	\[ - 1\]

The graph plotted for this point is represented below:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.