Question

How do you graph the function $f\left( x \right) = {\log _{10}}\left( x \right)$ ?

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 $f\left( x \right)$ 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 the given 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 $f\left( x \right)$ are real numbers. These pairs are in the cartesian form and the graph is the two-dimensional graph.
First, we have to find the value of y by using the graph equation $y = f\left( x \right) = {\log _{10}}\left( x \right)$ .
Let us substitute the value of x as $10$ .
$\Rightarrow y = {\log _{10}}\left( {10} \right)$
$\Rightarrow y = 1$
Now, we consider the value of x as $100$ , the value of y is
$\Rightarrow y = {\log _{10}}\left( {100} \right)$
$\Rightarrow y = 2$
Now we consider the value of x as $1$ , the value of y is
$\Rightarrow y = {\log _{10}}\left( 1 \right)$
$\Rightarrow y = 0$
Now we draw a table for these values we have

X	$10$	$100$	$1$
y	$1$	$2$	$0$

We also know the nature of the graph of logarithmic function. Hence, we can now plot the graph of the given function $y = f\left( x \right) = {\log _{10}}\left( x \right)$ . The graph plotted for these points 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.