Question

What is the nature of the graph: $y = \dfrac{4}{x}$
A.Rectangular hyperbola in first and third quadrant
B.Rectangular hyperbola in first and second quadrant
C.Hyperbola but not rectangular hyperbola
D.Rectangular hyperbola in second and fourth quadrant

Answer 1

Hint : This question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. We need to know how to draw a graph for the given equation. Also, we need to know how to find $x\& y$ from the given equation to make an easy calculation for the given question. Also, we need to know how to plot the points in the graph.

Complete step-by-step answer :
To find the nature of the graph we would draw the graph for the given equation.
For that, we would assume $x = ...., - 2, - 1,0,1,2,...$
We have $y = \dfrac{4}{x} \to \left( 1 \right)$
Let’s take $x = - 2$ in the equation $\left( 1 \right)$ , we get
$\left( 1 \right) \to y = \dfrac{4}{x}$

$$y = \dfrac{4}{{ - 2}} \\\ y = - 2 \;$$

Let’s take $x = - 1$ in the equation $\left( 1 \right)$ , we get
$\left( 1 \right) \to y = \dfrac{4}{x}$

$$y = \dfrac{4}{{ - 1}} \\\ y = - 4 \;$$

Let’s take $x = 0$ in the equation $\left( 1 \right)$ , we get
$\left( 1 \right) \to y = \dfrac{4}{x}$

$$y = \dfrac{4}{0} \\\ y = \infty \;$$

Let’s take $x = 1$ in the equation $\left( 1 \right)$ , we get
$\left( 1 \right) \to y = \dfrac{4}{x}$

$$y = \dfrac{4}{1} \\\ y = 4 \;$$

Let’s take $x = 2$ in the equation $\left( 1 \right)$ , we get
$\left( 1 \right) \to y = \dfrac{4}{x}$

$$y = \dfrac{4}{2} \\\ y = 2 \;$$

Let’s make a tabular column with various $x\& y$ values as given below,

$x$	$- 2$	$- 1$	$0$	$1$	$2$
$y$	$- 2$	$- 4$	$\infty$	$4$	$2$

By using the above tabular column we can make the following graph,

The above graph defines the equation $y = \dfrac{4}{x}$ . In the above graph, we can see that the rectangular hyperbola is present in the first quadrant and third quadrant.
So, the final answer is,
$A)$ Rectangular hyperbola in first and third quadrant
So, the correct answer is “OPTION A ”.

Note : This question describes the arithmetic operations like addition/ subtraction/ multiplication/ division. Note that to solve these types of questions we would draw the graph for the given equation. Also, note that for finding the value $y$ we have to assume the $x$ values. By using $x\& y$ values we can easily draw the graph.