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📈college algebra review

key term - Cubic functions

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Definition

A cubic function is a polynomial function of degree three, typically expressed in the form $f(x) = ax^3 + bx^2 + cx + d$, where $a$, $b$, $c$, and $d$ are constants and $a \neq 0$. These functions can have up to three real roots and exhibit distinct characteristics such as points of inflection.

5 Must Know Facts For Your Next Test

  1. Cubic functions can have one or three real roots.
  2. The graph of a cubic function has at most two turning points.
  3. There is always one point of inflection in the graph of a cubic function.
  4. The end behavior of cubic functions depends on the sign of the leading coefficient $a$; if $a > 0$, it rises to the right and falls to the left, and if $a < 0$, it falls to the right and rises to the left.
  5. Cubic functions are invertible on intervals where they are strictly increasing or decreasing.

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