Functions

Functions

1. Slope

   • Rise over Run
     • Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line.
   • Rate of Change
     • It can generally be expressed as a ratio between a change in one variable relative to a corresponding change in another; graphically, the rate of change is represented by the slope of a line.

2. Symmetry

   • Point symmetry
     • Point Symmetry is when every part has a matching part that is ... ... the same distance from the central point ... ... but in the opposite direction. It looks the same when viewed from opposite directions, such as left vs. right, or when turned upside down. Occurs when a function is odd
   • Line Symmetry
     • Another name for reflection symmetry. One half is the reflection of the other half. The "Line of Symmetry"s the imaginary line where you could fold the image and have both halves match exactly. Occurs when a function is even.

3. Extrema

   • Absolute Max
     • The highest point over the entire domain of a function or relation. Written as max:1 at x=1
   • Absolute Minimum
     • The lowest point over the entire domain of a function or relation. Written as Min: -1 at x=-1
   • Relative Max
     • the value of a function at a certain point in its domain, which is greater than or equal to the values at all other points in the immediate vicinity of the point. Written as Max:-1 at x=2
   • Relative Minimum
     • The lowest point in a particular section of a graph. Written as min 3 at x=2

4. Domain

   • X-Value
     • How left or right a point is in reference to the X-axis. It is the first number in an ordered pair (X,Y)
   • Input
     • The input of a function is what plugs into the equation to give you an output. Inputs are commonly written as X or another variable.

5. Range

   • Y-Value
     • How high or low a point is in reference to the Y-axis. It is the second number in an ordered pair (X,Y).
   • Output
     • The output of a function is what comes out when you plug in an input. Outputs are common written as y= or f(x)=

6. Limits

   • Limit from the left
     • a limit from the left restricts the domain variable to values less than the number the domain variable approaches. When a limit is taken from the left it is written
   • Limit from the right
     • a limit from the right restricts domain variable to values greater than the number the domain variable approaches. When a limit is taken from the right it is written

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