HCCSE MATH DEPT. 1 Revised Fall 2008


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1 FINAL EXAM REVIEW ITEMS Math : College Algebra Find the intercepts and an intercepts. ) f() = ) = Name ) Select the equation that describes the graph. Solve the equation and epress the solution in eact form. ) log ( + )  log (  ) = log ) Find (f  g)(7) when f() = + + and g() = Solve the nonlinear sstem of equations. ) + =  = 0 Decide whether the relation defines a function. ) A) = (  )  B) = (  ) + C) = ( + )  D) = ( + ) + 9) Find the distance between the points, and find the midpoint of the line joining them. (, ) and (, ) ) Use factoring to solve the equation: + = 0 Find the indicated composite for the pair of functions. ) (g f)(): f() =  + 9, g() = + Find an vertical asmptotes. ) f() =  + Evaluate the logarithm. 7) log 9 Solve the inequalit. Give the solution set in interval form. ) 79 < 7 7 HCCSE MATH DEPT. Revised Fall 00
2 Find an vertical asmptotes.  7 ) f() = + ) A rectangular Persian carpet has a perimeter of 0 inches. The length of the carpet is in. more than the width. What are the dimensions of the carpet? Decide whether or not the functions are inverses of each other. + ) f() =, g() = + 7) How man real zeros does this graph have? Write an equivalent epression in eponential form. ) log =  Give the domain and range for the rational function. Use interval notation. 9) f() = + 0) Find the equation of the parabola A) =  + B) = + + C) =   D) = +  ) Find g( + h)  g() when g() =  ) John owns a hotdog stand. His profit is represented b the equation P() = , with P being profits and the number of hotdogs sold. What is the most he can earn? ) Find f + g  if f() =  and g() = 9 + Write the epression as a sum, difference, or product of logarithms. Assume that all variables represent positive real numbers. ) log 9m Find the horizontal asmptote of the given function. ) f() = +  Find the requested value. ) f() for f() =, if  , if > 
3 Use the remainder theorem and snthetic division to find f(k). 7) k = ; f() = ) log = Give all possible rational zeros for the following polnomial. Solve. ) P() = ) +  =  9) Find the domain (D) and the range (R) for the function. Use snthetic division to perform the division. ) Find the zeros of the polnomial function and state the multiplicit of each. ) (  7) (  ) 7) Which of the following choices describes a linear function whose graph has a slope of? A) = + 9 B) = C) + = 0 D) f() =  + ) ( + )/ + ( + )/  0 = 0 Perform the requested operation or operations. 0) f() = , g() = 9 + Find (f + g)(). Graph the polnomial function. ) f() = ( + )( + ) Give all solutions of the cubic equation. )  = 0 Evaluate the determinant.  9) If f is onetoone, find an equation for its inverse. 0) f() = 7 + Find the slope of the line satisfing the given conditions. ) (, ) and (9, ) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. ) 9, , and + i A) f() = B) f() = C)f() = D) f() =
4 Solve the quadratic inequalit. Write the solution set in interval notation. )  Factor f() into linear factors given that k is a zero of f(). ) f() = ; k = ) + + = 0 ) The length of a rectangular frame is cm more than the width. The area inside the frame is square cm. Find the width of the frame. Find all rational zeros and factor f(). 7) f() = Solve and graph the inequalit. Give answer in interval notation. ) + < Decide whether or not the functions are inverses of each other. 9) f() = , g() = + Find the domain and range of the function. 0) = ( + ) + Graph the function. ) f() = 0 Find the matching description. ) f() = ( + ) A) Verte , 0 ; opens upward B) Verte 0,  ; opens downward C)Verte, 0 ; opens upward D) Verte 0, ; opens downward Find the determinant of the given matri. )  Solve the following equation for. )  = 7 Use the product, quotient, and power rules of logarithms to rewrite the epression as a single logarithm. Assume that all variables represent positive real numbers. ) loga q  loga r Use the factor theorem to decide whether or not the second polnomial is a factor of the first. ) ; + A) Yes B) No Solve the sstem b substitution. 7) + 7 = =  Solve the sstem b elimination. ) + =  + = 0 Solve and graph the inequalit. Give answer in interval notation. 9)  < Use snthetic division to decide whether the given number is a zero of the given polnomial. 0) ; f() = + + 
5 If f is onetoone, find an equation for its inverse. ) f() =  7 Evaluate the logarithm. ) log + ) = 9  ) A boat is 9 feet from the base of cliff. If the distance from the top of the cliff to the boat is feet less than twice the height of the cliff to the water. Find the height of the cliff. Round to the nearest tenth of a foot if necessar. ) Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone mi, the distance between the cars was mi more than the distance traveled b the car heading east. How far had the east bound car traveled? ) +  = 7) ( + )  ( + ) + = 0 Sketch the graph of the rational function. 7) f() = (  )( + ) Find the center and radius of the circle. 7) = 0 Use the intermediate value theorem to show that the polnomial has a real zero between the given values of a and b. 7) a =  and b =  f() = Use the product, quotient, and power rules of logarithms to rewrite the epression as a single logarithm. Assume that all variables represent positive real numbers. 7) log (  ) + log (  7) Solve the quadratic inequalit. Write the solution set in interval notation. ) Give the domain and range of the relation. 9) = + Find the centerradius form of the equation of a circle. 70) center (, 0), radius For the polnomial, one zero is given. Find all others. 7) P() = ;
6 Answer Ke Testname: FINALREVIEW ) intercept (0, 0), intercepts (, 0) and, 0 ) {} ) ) 07 ) {(, ), (, ), (, ), (, )} ) Function 7)  ) A 9) ; (, ) 0) , ± i ) ) None ) , 9 ) = 0, = ) Width: in.; length: 9 in. ) No 7) four )  = 9) Domain: (, ) (, ); Range: (, 0) (0, ) 0) A ) hh ) $7 ) 7 ) log 9 + logm  log ) = )  7) ) {} 9) D: (, ) (, ) R: (, ) (, ) 0)  + ) ) {,  ± i } ) ±, ±/, ±, ±9, ±7 )  ) ) Multiplicit : 0 Multiplicit : ± Multiplicit : 7 7) A ) {7, } 9) 7 0) f() = ) ) A ) [, ] ) (  )(  )( + ) ) ) cm  ± 7), , ; f() = (  )( + )(  ) ) (, 7) ) No 0) Domain: (, ); Range: [, ) ) ) A ) 7 ) {} ) loga q r ) B 7) {(, )} ) , 9) [, ) ) No ) f() = + 7 ) ) ) 9 feet ) 0 mi ) {} 7) {, , , } ) (, ] [7, ) 9) D = [, ); R = [0, ) 70) (  ) + = 7) + i,  i HCCSE MATH DEPT. Revised Fall 00
7 Answer Ke Testname: FINALREVIEW 7) ) (, ); r = 7 7) f(a) =  and f(b) = 7) log (  )(  7) 7
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