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# HW4 - find the equation of any horizontal vertical or slant...

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Page 1 of 2 Math 2312 Homework 4 Due: Wednesday, June 23, 2010, at the beginning of class 1. Given that one of the roots of f ( x ) is -1, sketch the graph of the function using the leading coefficient and the multiplicity of the zeros: 3 5 6 8 6 2 ) ( x x x x f 2. Divide: ) 2 3 ( ) 2 6 ( 2 2 4 x x x x 3. Find all the zeros of the function (and multiplicity if greater than one). (a) 9 24 12 ) ( 2 t t t r (b) 3 3 4 2 ) 1 ( ) 2 ( 4 ) 1 ( ) 2 ( 3 ) ( x x x x x f 4. Find all solutions of the equation 0 4 2 13 2 2 3 x x x 5. Find the open interval(s) on which the function in #3(b) is positive, and open interval(s) where it is negative. 6. For the function, ) 3 )( 1 ( 2 ) ( 2 x x x x f (a) state the domain, (b) identify all intercepts (give answers in ordered pair form), (c)

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Unformatted text preview: find the equation of any horizontal, vertical, or slant asymptotes. 7. Find the intervals where ) ( x f if 2 2 2 2 ) 9 ( 2 ) 4 ( ) 9 ( 2 ) ( x x x x x x f (hint: simplify, and perform a sign analysis) 8. A closed rectangular box with square base is shown below. If the volume of the box is to be 110 cubic centimeters, express the surface area S as a function of x . x y x Page 2 of 2 9. If 13 6 3 ) ( 2 x x x x f and 3 ) ( u u g , show that 2 1 ) 4 ( )) ( ( 2 u u u g f 10. Find the domain, in interval notation, for the function: 1 1 2 ) ( 2 x x x f...
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