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Goes from properties of quadratic functions to properties of their inverses.
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1. Identify the following for the functionf ( x )=−x2+10 x−32 :
i. Domainii. Range
iii. Roots/Zeroesiv. Factorsv. Sign chart
vi. IVT (or intervals where f ( x )≥0 and wheref ( x )<0)vii. Axis of symmetry
viii. Vertexix. Interval of max/min valuex. Is the function even or odd?
xi. Transformation given the function P ( x )=x2 [Hint: “complete the square” first]xii. What is the end behavior of the function?
xiii. Domain restrictionsxiv. Inverse of the function to the right of the vertexxv. Domain of the inverse
xvi. Range of the inversexvii. Prove f ( f −1 ( x ) )=f−1 (f ( x ) )=x numerically for this function.