Pre-Calc

Pre-Calc

1. Quadratics

   • Graphs
   • Formulas
     • f(x)=ax^2+bx+c
     • f(x) = a(x-h)^2+k
     • completing the square : x = -b _/b^2 -4ac / 2a

2. Linear Functions

   • Formulas
     • y=mx+b Examples: y=5x-3, f(t) = 3t. h(x)=x. y=3-x
     • Increasing if m>0 decreasing if m<0. constanct if m=0
     • Parallel. / not
       • f(x) = -2x+6. g(x)=-2x-4
       • f(x) = 3x+2. g(x)=2x-2
     • correlation coefficient
       • r>0 --> increasing
       • r<0 --> decreasing
       • closer to 0 = more scattered
       • closer to 1 or -1 = less scattered
   • Graphs

3. Function Behavior

   • Average rate of change
     • (y2 - y1) / (x2 - x1)
   • Piecewise functions (absolute functions)
     • |x|= x. x≥0. -x. x<0
   • Inverse Functions
     • f(x) = y, the inverse is f^-1(x)
       • f^-1(x) = 1/f(x)

4. Transformations

   • Vertical and horizontal transformations
     • shift stretch compress flip

5. Rational Functions

   • Vertical
     • x=0 as x approaches 0, f(x) tends to either infinity or - infinity
     • Removable Discontinuities
   • Horizontal
     • y=b, the graph approaches the line as the input increases/decreases without bound
   • Asymptotes
     • f(x) = ((x+1)^2 (x-3)) / ((x+3)^2 (x-2))
       • - at the x-int x=-1 corresponding to the (x+1)^2 factor the numerator, the graph bounces - at the x-int x=3 corresponding to the (x-3) factor the numerator, the graph passes through axis - at x=-3 corresponds to the (x+3)^2 factor of the the the denominator, the graph heads toward positive infinity on both sides - at x=2, corresponds to the (x-2) factor of the denominator, the graph heads to + infinity on the left & - infinity on the right

6. Composite Functions

   • Notation
     • f of g = f(g(x))
     • Domain
       • f(x) = 5/x-1 , g(x) = 4/3x-2. 4/3x-2 = 1. x=(- infinity, 2/3) U (2/3, 2) U (2,infinity)

Bilder und Dateien der Mindmap