Graph Hyperbolas

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Question 1 of 2

1. Question
Plot the graph with equation $y = \frac{1}{x}$ $y=\frac{1}{x}$ .
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The standard form for a hyperbola is $y = \frac{k}{x}$ $y=\frac{k}{x}$ or $y x = k$ $yx=k$ .

Create a table for $x$ $x$ and $y$ $y$ values, and fill in some sample values for $x$ $x$

$x$ $x$ $- 3$ $-3$ $- 2$ $-2$ $- 1$ $-1$ $0$ $0$ $1$ $1$ $2$ $2$ $3$ $3$

$y$ $y$

For each value of $x$ $x$ in the table, calculate $\frac{1}{x}$ $\frac{1}{x}$ and put this value in the cell below the $x$ $x$ -value.

When $x = \frac{1}{2}$ $x=\frac{1}{2}$ , we find $y$ $y$ by $\frac{1}{x} = \frac{1}{\frac{1}{2}} = 2$ $\frac{1}{x}=\frac{1}{\frac{1}{2}}=2$ .

When $x = 0$ $x=0$ , we cannot find $y$ $y$ , because $\frac{1}{x}$ $\frac{1}{x}$ is not defined, as we cannot divide by $0$ $0$ .

The completed table should be as shown below.

$x$ $x$ $- 3$ $-3$ $- 2$ $-2$ $- 1$ $-1$ $0$ $0$ $\frac{1}{2}$ $1/2$ $1$ $1$ $2$ $2$ $3$ $3$

$y$ $y$ $- \frac{1}{3}$ $-1/3$ $- \frac{1}{2}$ $-1/2$ $- 1$ $-1$ $2$ $2$ $1$ $1$ $\frac{1}{2}$ $1/2$ $\frac{1}{3}$ $1/3$

Plot the points in the table on a set of coordinate axes.

For example the first column tells us the point $(- 3, - \frac{1}{3})$ $(-3,-\frac{1}{3})$ should be plotted on the graph

The hyperbola will be made up of two parts in two separate quadrants. Draw a smooth curve through the points in the two quadrants.
Question 2 of 2

2. Question
Plot the graph with equation $y = \frac{- 2}{x}$ $y=\frac{-2}{x}$ .
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The standard form for a hyperbola is $y = \frac{k}{x}$ $y=\frac{k}{x}$ or $y x = k$ $yx=k$ .

Create a table for $x$ $x$ and $y$ $y$ values, and fill in some sample values for $x$ $x$

$x$ $x$ $- 3$ $-3$ $- 2$ $-2$ $- 1$ $-1$ $0$ $0$ $1$ $1$ $2$ $2$ $3$ $3$

$y$ $y$

For each value of $x$ $x$ in the table, calculate $\frac{- 2}{x}$ $\frac{-2}{x}$ and put this value in the cell below the $x$ $x$ -value.

When $x = 0$ $x=0$ , we cannot find $y$ $y$ , because $\frac{- 2}{x}$ $\frac{-2}{x}$ is not defined, as we cannot divide by $0$ $0$ .

The completed table should be as shown below.

$x$ $x$ $- 3$ $-3$ $- 2$ $-2$ $- 1$ $-1$ $0$ $0$ $1$ $1$ $2$ $2$ $3$ $3$

$y$ $y$ $\frac{2}{3}$ $2/3$ $1$ $1$ $2$ $2$ $- 2$ $-2$ $- 1$ $-1$ $- \frac{2}{3}$ $-2/3$

Plot the points in the table on a set of coordinate axes.

For example the first column tells us the point $(- 3, \frac{2}{3})$ $(-3,\frac{2}{3})$ should be plotted on the graph

The hyperbola will be made up of two parts in two separate quadrants. Draw a smooth curve through the points in each of the two quadrants.

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1. Question

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2. Question

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Quizzes

$x$ $x$	$- 3$ $-3$	$- 2$ $-2$	$- 1$ $-1$	$0$ $0$	$1$ $1$	$2$ $2$	$3$ $3$
$y$ $y$