Question

How do you sketch the graph of $f\left( x \right) = \arccos \left( x \right)$ ?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of 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 answer:
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 value of y by using the equation of function $y = f\left( x \right) = \arccos \left( x \right)$. Let us substitute the value of x has \[ - 1\], \[0\], and $1$.
Now we consider the value of x as \[ - 1\], the value of y is
$ \Rightarrow y = \arccos \left( { - 1} \right)$
$ \Rightarrow y = \pi $
Now we consider the value of x as \[0\], the value of y is
$ \Rightarrow y = \arccos \left( 0 \right)$
$ \Rightarrow y = \dfrac{\pi }{2}$
Now we consider the value of x as $1$, the value of y is
$ \Rightarrow y = \arccos \left( 1 \right)$
$ \Rightarrow y = 0$
Now we draw a table for these values we have

x	\[0\]	\[1\]	\[ - 1\]
y	\[\dfrac{\pi }{2}\]	\[0\]	\[\pi \]

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.