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.