27 lines
1.0 KiB
Markdown
27 lines
1.0 KiB
Markdown
# Notes
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## Composition of functions
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For $(f\circ g)(x)$ for two sets, you look for $x$ from $f$ and an equivalent $y$ value from $g$, and leftover coordinates are the answer. The order of $f$ and $g$ does matter.
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# Formulae
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The general equation for a circle:
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$$ (x - h)^2 + (y - k)^2 =r^2 $$
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Distance formula:
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$$ \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} $$
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Midpoint formula:
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$$ (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) $$
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Adding functions:
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$$ (f + g)(x) = f(x) + g(x) $$
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Multiplying functions:
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$$ (f*g)(x)=f(g(x)) $$
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# Examples
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Given the function $f = \{(0, 2), (3, -1), (5, 4), (2, 1)\}$, and $g=\{(2, 0), (3, -1), (4, -2), (5, 2)\}$, and applying $(f+g(x)$, If the same $x$ value exists in both the sets $f$ and $g$, then you can solve for that value by adding $y$ values for the matching x coordinates together.
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# Terminology
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| Term | Definition |
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|--|--|
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| $h$ | How far left or right something is shifted from the origin |
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| $k$| How far up or down something is shifted from the origin |
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| $r$ | The radius of a circle |
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