Chapter 14, Problem 1RVS

To determine

The correct match of the equation $xy=2$ from the provided graph (a) to (j).

Answer to Problem 1RVS

Solution:

The graph of the equation $xy=2$ is

The correct option is (j).

Explanation of Solution

Given Information:

The provided equation is $xy=2$.

The given options are,

Consider the equation $xy=2$.

Since, $xy=k$ is the standard form of rectangular hyperbola of which asymptotes are the coordinate axes.

If $k>0$ then, the function is decreasing from zero to negative infinity and from positive infinity to zero. That is the graph of the rectangular hyperbola opening in the first and third quadrants.

Therefore, $xy=2$ is the equation of the Rectangular Hyperbola.

Here, $k=2>0$, so the graph of the rectangular hyperbola opening in the first and third quadrants.

To draw the graph, find the solutions of the equations.

Consider the equation $xy=2$

Put $x=1$, in the equation $y=\frac{2}{x}$

$\begin{array}{c}y=\frac{2}{x}\\ =\frac{2}{1}\\ =2\end{array}$

Also, put $x=2$, in the equation $y=\frac{2}{x}$

$\begin{array}{c}y=\frac{2}{x}\\ =\frac{2}{2}\\ =1\end{array}$

So, $\left(1,2\right)$ and $\left(2,1\right)$ is the solution of the equation $xy=2$.

Similarly, $\left(-1,-2\right)$ and $\left(-2,-1\right)$ is also the solution of the equation $xy=2$.

To make the graph, plot the points $\left(1,2\right)$, $\left(2,1\right)$, $\left(-1,-2\right)$ and $\left(-2,-1\right)$.

$x$	$y=\frac{2}{x}$
1	2
2	1
$-1$	$-2$ 0
$-2$	$-1$

Hence, the correct answer is graph (j).