chapter 3 - equations and inequalities/chapter 4 - graphs and transformations
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| quadratic inequalities | solved by substituting the linear equation into the quadratic one
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| simultaneous equations on graphs | the points at which the graphs intersect are solutions to the simultaneous equations
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| inequalities | the set of values in which a condition is satisfied (e.g one equation being greater than another one)
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| 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)”
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| 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
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| 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)
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| 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)
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| 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
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| 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
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| reciprocal functions (y=k/x^n) | have an asymptote at the axis
if n is even, will be symmetrical across the y-axis
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| 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
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| 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)
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| 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
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Or sort by any of the columns using the down arrow next to any column heading.
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Created by:
That cool NAMe
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