1.0 KiB
1.0 KiB
Notes
Composition of functions
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.
Formulae
The general equation for a circle:
(x - h)^2 + (y - k)^2 =r^2
Distance formula:
\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}
Midpoint formula:
(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})
Adding functions:
(f + g)(x) = f(x) + g(x)
Multiplying functions:
(f*g)(x)=f(g(x))
Examples
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.
Terminology
| Term | Definition |
|---|---|
h |
How far left or right something is shifted from the origin |
k |
How far up or down something is shifted from the origin |
r |
The radius of a circle |