- Relations: Sets of (x, y) coordinates
- Functions: Relations where each input gives exactly one output
- Functional notation: Explore what f(x) means, and evaluate functions
- Continuity and smoothness: Some functions end and others keep going
- Describing functions: Make your own functions, and live to tell the tale
- Concavity: Math-talk for curvy
- Odd and even functions: Turns out functions can be "odd" and "even" too
A relation is any set or collection of ordered pairs (x, y) in coordinate system which, the set of x-values defines the domain and the set of y-values defines the range.
Special relations where every x-value (input) corresponds to exactly one y-value (output) are called functions.
Continuity – a function is continuous if you can draw it without picking up your pen.
Smoothness – a function is smooth if it’s continuous and doesn’t have any pointy corners.
A function is positive where its outputs are positive
A function is negative where its outputs are negative
The function is increasing if y goes up
The function is decreasing if y goes down
If a function is always increasing, then it’s monotonically increasing
If a function is always decreasing, then it’s monotonically decreasing
A function is concave up if it’s like smiling face symbol
A function is concave down if it’s like frowning face symbol
A point of inflection is where a function switches concavity
A function is odd f(-x) = -f(x)
A function is even f(-x) = f(x)
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