Question

How do you graph \[y = \dfrac{1}{{x - 4}}\]?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as \[y = f(x)\], 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 \[y = f(x)\], 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 graph equation \[y = \dfrac{1}{{x - 4}}\]. Let us substitute the value of x has -3, -2, -1, 0, 1, 2, and 3.
Now we consider the value of x as -3, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{ - 3 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{7} \\
   \Rightarrow y = - 0.142 \;
 \]
Let we round off the value of y we have y = -0.14
Now we consider the value of x as -2, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{ - 2 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{6} \\
   \Rightarrow y = - 0.167 \;
 \]
Let we round off the value of y we have y =- 0.17
Now we consider the value of x as -1, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{ - 1 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{5} \\
   \Rightarrow y = - 0.2 \;
 \]
Now we consider the value of x as 0, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{0 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{4} \\
   \Rightarrow y = - 0.25 \;
 \]
Now we consider the value of x as 1, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{1 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{3} \\
   \Rightarrow y = - 0.333 \;
 \]
Let we round off the value of y we have y = -0.3
Now we consider the value of x as 2, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{2 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{2} \\
   \Rightarrow y = - 0.5 \;
 \]
Now we consider the value of x as 3, the value of y is
\[
   \Rightarrow y = \dfrac{1}{{3 - 4}} \\
   \Rightarrow y = \dfrac{{ - 1}}{1} \\
   \Rightarrow y = - 1 \;
 \]
Now we draw a table for these values we have

X	-3	-2	-1	0	1	2	3
y	-0.14	-0.17	-0.2	-0.25	-0.3	-0.5	-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.