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# inequalities/graphs

### chapter 3 - equations and inequalities/chapter 4 - graphs and transformations

Term | Definition |
---|---|

quadratic inequalities | solved by substituting the linear equation into the quadratic one |

simultaneous equations on graphs | the points at which the graphs intersect are solutions to the simultaneous equations |

inequalities | the set of values in which a condition is satisfied (e.g one equation being greater than another one) |

set notation | {variable ∈ domain of variable (can be omitted if its the reals): condition on variable} can be used with U/n to combine multiple sets together “a variable in the set of (domain) such that the variable follows (condition)” |

inequalities with a variable | when multiplying by a variable, unless otherwise stated, multiply by it’s square to ensure that the inequality is not multiplied by a negative |

inequalities on a graph | f(x) > g(x) forms the set of points that on the functions such that f(x) is higher than g(x) |

shading inequalities | the shaded area often represents the final inequality, with dashed lines used for equations that are not a part of it (solid lines if they are) |

cubic functions | a polynomial in which the index is 3, contains a maximum of 2 turning points the limits as x approaches the infinities will always be infinities with different signs |

quartic functions | a polynomial in which the index is 4, contains a maximum of 2 turning points the limits as x approaches the infinities will always be infinities with the same sign |

reciprocal functions (y=k/x^n) | have an asymptote at the axis if n is even, will be symmetrical across the y-axis |

translations | f(x+a) represents a translation of moving the graph left a units f(x) + a represents a translation of moving the graph up a units |

stretches | f(ax) represents a stretch parallel to the x axis by a factor of 1/a (a=-1 is a reflection in the y-axis) af(x) represents a stretch parallel to the y axis by a factor of a (a=-1 is a reflection in the x-axis) |

transformations generally | manipulating a function in a way such that the function, all the points within it and any asymptotes it may have all “move” the same way |