Functions

Functions

1. Extrema

   • Relative Maximum: Also known as local max, the highest point in the given area
   • Absolute Maximum: The highest point throughout the entire graph
   • Relative Minimum: Also known as the local min, the lowest point in the given area
   • Absolute Minimum: The lowest point throughout the entire graph

2. Symmetry

   • Line Symmetry: when a function is symmetrical over the y axis
     • f(x)=Square Root of x^2-1
   • Point Symmetry: when a function is symmetrical about the origin
     • F(x)=-x^3+7x has point symmetry

3. Slope

   • Rise Over Run: to find the slope when looking at a function you use rise over run to find it
     • The rise here is 4 and the run is three, creating a slope of 4/3
   • y=mx+b: The m in the slope-intercept form is the slope
     • The m in Y=mx+b is the slope
   • Average Rate of Change: The change in the y value divided by the change in the x value for two distinct points on the graph
     • The average rate of change is the slope of a function

4. Domain

   • Left to Right (Run)
     • In a graph the domain is left to right (x value) it is the run when finding slope
   • Discontinuity: When a function does not continue completely through from the beginning to the end
     • There is a discontinuity at x= -1

5. Range

   • End Behavior: of the graph of y as x approaches positive infinity or negative infinity
     • End behavior and range are both measured with y values
   • Up and Down (Rise)
     • In a graph range is up and down (y value), it is the rise when finding slope

6. Limits

   • Limit Notation
     • Use this notation when finding limits
   • DNE (does not exist)
     • Jump
       • The limit DNE at x sub 0 due to the jump
     • Vertical Asymptote
       • The limit DNE at x=3 due to the vertical asymptote

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