The Hyperbola
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Question 1 of 5
1. Question
Plot the graph with equation `y=\frac{1}{x}`.Hint
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Well Done!
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The standard form for a hyperbola is `y=\frac{k}{x}` or `yx=k`.Create a table for `x` and `y` values, and fill in some sample values for `x``x` `-3` `-2` `-1` `0` `1` `2` `3` `y` For each value of `x` in the table, calculate `\frac{1}{x}` and put this value in the cell below the `x`-value.When `x=\frac{1}{2}`, we find `y` by `\frac{1}{x}=\frac{1}{\frac{1}{2}}=2`.When `x=0`, we cannot find `y`, because `\frac{1}{x}` is not defined, as we cannot divide by `0`.The completed table should be as shown below.`x` `-3` `-2` `-1` `0` `1/2` `1` `2` `3` `y` `-1/3` `-1/2` `-1` `2` `1` `1/2` `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})` 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.
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Question 2 of 5
2. Question
Write the equation of the cubic graph shown on the number plane below.
Hint
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Fantastic!
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The standard form of the equation of a hyperbola is `y=\frac{k}{x}` or `yx=k`.Use the point `(2,-3)` shown on the graph to find the value of `k`.The `x`-coordinate of this point is `2`, and the `y`-coordinate of this point is `-3`.So we should substitute `x=2` and `y=-3` into the equation `y``x``=k`, and solve to find `k`.`-3``\cdot``2``=k`.`k=-6`Substitute the value for `k` and write the equation of the graph.`y=\frac{-6}{x}` -
Question 3 of 5
3. Question
Plot the graph with equation `y=\frac{-2}{x}`.Hint
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Nice Job!
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The standard form for a hyperbola is `y=\frac{k}{x}` or `yx=k`.Create a table for `x` and `y` values, and fill in some sample values for `x``x` `-3` `-2` `-1` `0` `1` `2` `3` `y` For each value of `x` in the table, calculate `\frac{-2}{x}` and put this value in the cell below the `x`-value.When `x=0`, we cannot find `y`, because `\frac{-2}{x}` is not defined, as we cannot divide by `0`.The completed table should be as shown below.`x` `-3` `-2` `-1` `0` `1` `2` `3` `y` `2/3` `1` `2` `-2` `-1` `-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})` 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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Question 4 of 5
4. Question
Write the equation of the cubic graph shown on the number plane below.
Hint
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Exceptional!
Incorrect
The standard form of the equation of a hyperbola is `y=\frac{k}{x}` or `yx=k`.Use the point `(5,-4)` shown on the graph to find the value of `k`.The `x`-coordinate of this point is `5`, and the `y`-coordinate of this point is `-4`.So we should substitute `x=5` and `y=-4` into the equation `y``x``=k`, and solve to find `k`.`-4``\cdot``5``=k`.`k=-20`Substitute the value for `k` and write the equation of the graph.`y=\frac{-20}{x}` -
Question 5 of 5
5. Question
Write the equation of the cubic graph shown on the number plane below.
Hint
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Excellent!
Incorrect
The standard form of the equation of a hyperbola is `y=\frac{k}{x}` or `yx=k`.Use the point `(2,4)` shown on the graph to find the value of `k`.The `x`-coordinate of this point is `2`, and the `y`-coordinate of this point is `4`.So we should substitute `x=2` and `y=4` into the equation `y``x``=k`, and solve to find `k`.`4``\cdot``2``=k`.`k=8`Substitute the value for `k` and write the equation of the graph.`y=\frac{8}{x}`