COLLEGE ALGEBRA REVIEW FOR TEST 3

Transcription

1 COLLEGE ALGEBRA REVIEW FOR TEST If the following is a polnomial function, then state its degree and leading coefficient. If it is not, then state this fact. ) a) f() = b) f() = + 9 Provide the requested response. ) Use the graph of p() to determine the following: a) the number of turning points b) the -intercepts c) the sign of the leading coefficient d) the minimum degree of p() Determine an local or absolute etrema as indicated. ) Use the graph of f to estimate the local etrema ) a) f() = b) g() = + c) h() = ( + 5) - Use the graph to determine if f is odd, even, or neither. 5) a) b) Solve the problem. ) a) Complete the table if the function f is even. - f() -? -? b) Complete the table if the function g is odd. - 0 g() -9?? Determine whether the function is odd, even, or neither. 7) a) f() = - b) g() = - 5 c) h() = d) j() = + + ) f()

2 Review for Test Page Use the graph of f() = - 5 Pick which graph satisfies the given conditions. and translations of graphs ) Cubic polnomial with two distinct real zeros to sketch the graph of the equation. and a positive leading coefficient. 9) = f() - A) B) 0) = -f( - ) C) - State the end behavior of the graph of f. ) a) f() = - 9 b) g() = + + c) h() = - - d) n() = -

3 Review for Test Page ) Degree with turning points at (, -0),(-, Provide an appropriate response. ) and (0,-0). 7) Use long division to epress the (Dividend) as (Divisor)(Quotient) + (Remainder). A) Use snthetic division to divide the first polnomial b the second. ) a) ; + b) ; - c) ; - B) Solve the problem. 9) Use the figure to find the length L of the rectangle from its width and area A. Determine L when = feet. + A = C) Use the given information about the polnomial function f() to write its complete factored form. 0) Degree ; zeros:,, -; leading coefficient = L ) Degree ; zeros: -,,, - ; leading coefficient = Evaluate the function f at the indicated value and graph the function. ) g() for g() = -, if <, if + 5, if < Write the complete factored form of the polnomial f(), given the indicated zero. ) a) f() = ; - is a zero. b) g() = ; is a zero. Divide. Write with positive eponents. 5) Divide. ) a) ; - 7 b) ; +

4 Review for Test Page The graph of the polnomial f() is shown in the figure. Find the zeros of f(), given that one zero is k. Estimate the zeros and state whether their multiplicities are odd or even. ) 0 9) f() = ) f() = k = - k = 9 ) Write a polnomial f() in complete factored form that satisfies the conditions. Let the leading coefficient be. 5) Degree ; zeros: with multiplicit, and 7 with multiplicit Use the rational zero test to list all possible rational zeros of f(), then find the zeros. ) f() = Solve the polnomial equation smbolicall. 7) a) - = 0 b) - - = 0 c) = 0 Find the complete factored form of the polnomial f() that satisfies the given conditions. Then write the polnomial in epanded form. ) Degree, leading coefficient 5, zeros at i and i ) f() = k = ) f() = k = -i Epress f() in complete factored form. ) a) f() = + b) g() = + c) h() = d) p() = e) q() = Solve the polnomial equation. ) = 0 5) = 0 Find the domain of f. 7 ) a) f() = - - b) g() = + 9 (- )( + ) c) h() = - Find an vertical and horizintal asmptotes. 7) a) f() = b) f() = - - c) f() = Write a smbolic representation of a rational function f that satisfies the conditions. ) Vertical asmptotes = and = -, horizontal asmptote = Sketch the graph of the rational function. 9) f() = - + 5

5 Review for Test Page 5 Solve the equation. 0) m - m = 5 Use radical notation to rewrite. 5) a-/b/7 ) b + b - = b - b - Solve the rational equation. ) = 5 - ) = 7 Solve the polnomial inequalit. ) ( - )( - )( - 7) > 0 Use translations of the graph of f() = to help sketch a graph of g. 5) g() = - + Solve the equation. 5) q - 7 = 7 5) - = - 55) - 5 = 5 + 5) / = 5) Use the graph of the rational function f to solve the inequalit. ) Solve f() > ) / - 9 = 0 Solve the problem. 5) One stud showed that for a male fiddler grab weighing over 0.75 gram, the weight of its claws can be estimated b w() = 0.5.5, where is the weight of the crab in grams and w is the weight of the claws in grams. Round our answers to the nearest hundredth of a gram. a) Predict the weight of the claws of a -gram crab. b) Approimate the weight of a crab that has 0.-gram claws. Solve the rational inequalit. 7) - + > 0 ) + > 5 9) - - Use positive rational eponents to rewrite the epression. 50) 5

6 Answer Ke Testname: CAREVIEW_F0 ) a) Degree: 9; leading coefficient: b) Not a polnomial function ) a) turning points b),, 0,, c) positive d) minimum degree = 5 ) Local maimum: appro..0; local minima: appro and.75 ) a) No local etrema; no absolute etrema b) Local minimum: ; absolute minimum: c) Local maimum: -; absolute maimum: - 5) Odd, Even ) a) -, - b) 0, 9 7) a) Even b) Neither c) Odd d) Neither ) Even 9) 0) ) a) Up on both sides b) Down on left side, up on right side c) Down on both sides d) Up on left side, down on right side ) B ) C ) a) g() = b) ) ) a) - 9 b) ) ( - )( + - ) - ) a) b) c) ) 5 + ; 7 ft 0) f() = ( - )( - )( + ) ) f() = + ( - )( + ) + ) a) f() = ( + )( - )( + ) b) g() = - ( - )( + ) - ) (odd), - (even), (odd) ) (odd), - (odd), (even), (odd) 5) f() = ( + )( - 7) ) Possible zeros: ±, ±, ±, ±, ±, ± Zeros:,, -/ 7) a) = 0,, - b) =, - c) = 0,, ) factored form: f() = 5( - i)( + i) epanded form: f() = ) -, ± 0) 9, ±i ), 5 ± i ) ±i, ±

7 Answer Ke Testname: CAREVIEW_F0 ) a) f() = ( + i)( - i) b) g() = ( + i )( - i ) c) h() = 5( + i)( - i) d) p() = ( + 9)( + i)( - i) e) q() = ( + 5)( - )( + i)( - i) ) = -, i, i 5) =,, -i, i ) a) { } b) { 0, -9} c) { ±} 7) a) V.A.: = ; H.A.: = 7 b) V.A.: =, = -; H.A.: = 0 c) V.A.: =, = -7; H.A.: none ) Answers ma var. Possible answer: f() = 9) + ( - ) ( + ) 0 5) 5) 7 5) 55) -7 5) ) 5) a) f() =.0 grams b) about. grams ) {-, } ) {} ), ) - ) (, ) (7, ) 5) (-, -5] [-, -] ) (-, ) (0, 5) 7) (-, -) (, ) ), ) [-5, ) (, ) 50) /5 5) 7 b a