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# inequalities/graphs

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

TermDefinition
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
Created by: That cool NAMe
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