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# fall 2006 - 1800F061 MAT 1800 Final Exam SHOW ALL WORK IN A...

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1800F061 MAT1800FinalExam SHOWALLWORKINABLUEBOOK: Onlyminimalcreditwillbeawardedforanswerswithoutsupportingwork. 1. (8pts.) Graphandfindtherange of: f ( x )= x 2 if 0 x< 3 x +2 if 1 <x< 0 4 x 2 if 3 <x ≤− 2 2. (8pts.) Findthedomainofthefunctiongivenby: f ( x )= 4 x 2 +3 x. 3. (12pts.) Let f ( x )= x 2 4 x +7 and g ( x )=5 3 x. Findandsimplifycompletely: (a) ( g f )( x ) (b) f ( x + h ) f ( x ) h 4. (8pts.) Let f ( x )= x +1 x 2 . Find f 1 ( x ) , where f 1 istheinversefunctionof f. 5. (10pts.) Anopenboxistobemadeofarectangularpieceofmaterial,15inchesby9inches, bycuttingequalsquaresfromthecornersandturingupthesides. Let x representthelength of the sides of the squares removed. Express the volume V of the box as a function of x . Alsograph y = V ( x ) . 6. (10pts.) Amanufactureroflightingfixtureshasdailyproductioncostsof C = 1 4 x 2 10 x +800 where C is the cost (indollars)and x is thenumberof units produced. Howmanyfixtures shouldbeproducedeachdaytoyieldaminimumcost?

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