Functions

Functions

1. Symmetry

   • y=x is the reflection functions make to form their inverses
   • Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction
   • If you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror-image halves

2. Slope

   • Slope of a function describes the activity of the line
   • Can be negative or positive, compressed, stretched, etc.

3. Limits

   • Limit notation end-behavior states where the y-value is approaching at any given x-value
   • Written as lim f(x) x->?
   • Can be altered by shifts like phase shifts and compressions
   • Can be dictated by whether or not the function is continuous or discontinuous like a piecewise function
     • A discontinuity is point at which a mathematical object is discontinuous. The left figure above illustrates a discontinuity in a one-variable function while the right figure illustrates a discontinuity of a two-variable function

4. Domain

   • All values of x that define the function and make up the input
   • Includes x-integers on a graph ranging from negative infinity to positive infinity

5. Extrema

   • Relative Maximum: The point on a graph that appears to be the highest reaching y-value
   • Absolute Maximum: Usually infinity being the highest area on a graph
   • Relative minimum: Point on a graph appearing to be the lowest point
   • Absolute minimum: Usually negative infinity since it is absolutely negative

6. Range

   • All values of y that make up the output
   • Includes y-integers on the y-axis ranging from negative infinity to positive infinity

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