5B - Introduction to non-linear graphs
In the following sections we will examine the graphs and transformations of the hyperbola, truncus, and square root functions as well as circles and semi-circles.
The hyperbola function: \[y=\frac{1}{x}\]
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The truncus function: \[y=\frac{1}{x^2}\]
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The square root function: \[y=\sqrt{x}\]
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Key features:
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Key features:
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Key features:
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The circle: \[x^2+y^2=r^2\]
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The semicircle: \[y=\pm \sqrt{r^2-x^2}\]
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Like linear and quadratic graphs, the power relations above have a standard basic shape which is simply dilated, reflected and/or translated when undergoing transformations. These graphs, and their transformations, will be explored in the following sections.