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Level 378

Rational Functions & Recursion


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a(x+d)^2+e=0
completing the square
Vertical Asymptotes
zeroes of denominator
Horizontal Asymptotes
y=0 when degree of denominator > degree of numerator
X-intercepts
the point on a graph where y = 0, also points where the graph crosses the x-axis
both pieces go in the same direction
asymptote comes from factor with even multiplicity
y-intercept
the point where the line crosses the y-axis
Holes
when same factor occurs in numerator and denominator
coordinates of holes
find zeroes of holes and plug into the equation with the holes cancelled out
no x-intercept
can't solve for zeroes in numerator
no vertical asymptote
can't solve for zeroes in denominator
oblique asymptotes
when degree in numerator > degree in denominator
recursion
can not be evaluated for a particular input value resulting in a single output value
closed form functions
can be evaluated for a particular input value resulting in a single output value
iteration
current value determines next value
recursion on calculator
MODE --> SEQ
equilibrium
make A(n) and A(n-1) equal and solve