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.