Using a spreadsheet to find x and y values for the function 
and plotting the points, gives the graph of a hyperbola (plural is hyperbolas or hyperbolae).
The hyperbolas studied at this level are called rectangular hyperbolas because the asymptotes are vertical and horizontal.
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From the spreadsheet, the points can be plotted on a graph. Note that the value when x = 0 cannot be calculated and the line x = 0 is known as the vertical asymptote. The horizontal asymptote is the x axis, y = 0
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As x gets nearer to being 0, the y value gets either very large or very small and the curve gets very close to the y axis but never touches it. |
The Basic Hyperbola
Equations of the type xy = c or 
have graphs which are hyperbolas.
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Example 1
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Example 2
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xy =5
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| Note: The bigger the value of c, the steeper the graph. | Note: If c is negative the graph is in the 2nd and fourth quadrants. |
Transformation of the Basic Hyperbola
As with parabolas, circles and cubics some equations can be graphed using the transformation approach.
Example 1 
. This is the hyperbola 
moved 2 units up the y-axis.
Example 2 
This is the basic hyperbola xy = 10 with the asymptotes moved forward 3 and down 4.
The Hyperbola as an Algebraic Fraction (Preparation for Year 13)
is a common form of an equation which has a hyperbola as its graph.
There are four main steps to sketching a graph of this type:
Example: Sketch the graph of  |
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Step 1: Find the y-intercept
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Put x = 0
y-intercept is (0, -3) |
| Step 2: Find the x-intercept |
Put y = 0
x-intercept is (-1.5, 0) |
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Step 3: Find the vertical x-asymptote.
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Put the denominator = 0 x − 1 = 0 The x-asymptote is x = 1 |
| Step 4: Find the horizontal y-asymptote |
The y asymptote is found by dividing out the fraction. y-asymptote is The y-asymptote is y = 2 |
| Sketch the graph |
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