Functions Flashcards
Compound Interest Formula
f(t) = P (1 + r/n)nt
logb1 =
0
logbb =
1
logbbp =
p
logbMN =
logbM + logbN
logb(M/N) =
logbM - logbN
logbMp =
p logbM
Exponential Growth or Decay Formula
f(t) = a(1 + r)t
- a is the current or initial count
- r is the growth or decay rate
- t is time.
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Absolute Value Function
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Cubic Function
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Identity Function
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Linear Function
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Square Root Function
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Quadratic Function
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Logarithmic Function
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Exponential Function
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Step Function
Rule for translating a function horizontally
f(x ± k)
- k shifts right
- k shifts left
Rule for translating a function vertically
f(x) ± k
- k shifts up
- k shifts down
Rule for stretching or compressing a function vertically
(k × f(x))
- k > 1, stretch
- 0 k < 1, compress
- - k, reflected about x-axis
Rule for stretching or compressing a function horizontally
( f(k × x))
- k > 1, compress
- 0 k < 1, stretch
- k, reflected about y-axis
Theorem that states every non-constant, single variable polynomial has exactly as many roots as the polynomial’s highest exponent.
Fundamental Theorem of Algebra
Theorem which states that if a polynomial finction f(x) is divided by a binomial x-a, where a is a real number, the remainder of the division will be the value of f(a). If f(a) = 0, then a is a root of the polynomial.
Remainder Theorem
Theorem which states that if f(a) = 0 then (x - a) is a factor of the function.
Factor Theorem