Find the distance between the pair of points. 1) (5, 4) (-7, -3) A) 193 B) 84 C) 5 D) 95

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1 Azu Onwe Okwechime (Instructor) HCCS - NORTHWEST COLLEGE PRECALCULUS - MATH - EXAM # SAMPLE- REVIEW. Eam will consist of to 6 chosen from these Questions MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the distance between the pair of points. ) (, ) (-7, -) A) 9 B) 8 C) D) 9 ) Solve. ) The graph shows an idealized linear relationship for the average monthl paments to retirees from 99 through 999. Use the midpoint formula to estimate the pament for Average Monthl Paments to Retiree Pament 60 0 a b Year a = $; b = $ ) A) 88 dollars B) 00 dollars C) 6 dollars D) dollars Graph the circle. ) ( - ) + ( - ) = 9 )

2 A) B) C) D) Find the center and radius of the circle. ) = 0 A) (6, ); r = B) (-6,-); r = 9 C)(-, -6); r = 9 D) (, 6); r = ) Determine the intervals over which the function is decreasing, increasing, and constant. ) 0 ) A) Increasing [, ); Decreasing [-, ); Constant (-, ) B) Increasing [, ); Decreasing (-, -]; Constant [-, ] C) Increasing (-, ]; Decreasing(-, -]; Constant (-, ) D) Increasing (-, ]; Decreasing [-, ); Constant [-, ]

3 Find the average rate of change illustrated in the graph. 6) 6) 0 Value of Car (in thousands of dollars) Year A) -$ per ear B) $ per ear C) $ per ear D) -$ per ear Write the equation of the line. 7) Through (-6, -7) parallel to = 6 A) = B) = C) = D) = ) 8) Through (9, -), perpendicular to - - = -9 A) = B) = - 6 C) = D) = - 6 8)

4 Refer to the following graphs to determine an appropriate response. Graph A Graph B Graph C Graph D - - 9) Which one is the graph of = [[]]? What is the value of when =.? A) Graph D; B) Graph A;. C)Graph B;. D) Graph C; 9)

5 Refer to the following graphs to determine an appropriate response. Graph A Graph B Graph C Graph D - - 0) Which one is the graph of =? What is it's domain? A) Graph A; (-, ) B) Graph D; [0, ) C)Graph C; {-,-, 0,, } D) Graph B; [0, ) 0)

6 Refer to the following graphs to determine an appropriate response. Graph A Graph B Graph C Graph D - - ) Which is not the graph of a function? What is its equation? A) Graph C; = B) Graph A; = C)Graph B; = D) Graph D; = [[]] ) 6

7 Refer to the following graphs to determine an appropriate response. Graph A Graph B Graph C Graph D - - ) Which one is the graph of =? What is its range? A) Graph D; [0, ) B) Graph C; [-, ] C)Graph B; (-, ) D) Graph A; (-, ) ) Find the requested value. ) 6, if - f(-) for f() = -, if > - A) B) - C) D) -6 ) Determine if the function is even, odd, or neither. ) f() = A) Neither B) Odd C) Even ) ) f() = - + A) Neither B) Even C) Odd ) 7

8 Perform the requested operation or operations. 6) f() = +, g() = 6 - Find (fg)(). A) ( + )(6 - ) B) ( + )( - ) C)( + )( 6 - ) D) ( - )( + ) 6) 7) f() = 9-7, g() = f Find g (). 7) A) B) 9-8 C) 9 + D) ) f() = + + 7, g() = - Find (g f)(). A) + + B) C)0 + + D) + + 9) f() = -, g() = -9 + Find (f + g)(). A) + 8 B) - C) -9 + D) ) 9) Find the domain and range of the indicated function. 0) Find the domain and range of (fg)() when f() = + and g() = - 6. A) Domain:, ; range: (0, ) B) Domain: -, ; range: (-, ) C)Domain:, ; range: (-, ) D) Domain:, ; range: [0, ) Compute and simplif the difference quotient ) l() = 6 - f( + h) - f(), h 0. h A) -( + h + h) B) -8 C) -( - - h) D) -( - h - h) 0) ) Find the indicated composite for the pair of functions. ) (g f)(): f() = + + 6, g() = - 7 A) B) C) D) + - ) Consider the function h as defined. Find functions f and g so that (f g)() = h(). ) h() = + A) f() = -, g() = + B) f() =, g() = + C)f() =, g() = + D) f() = -, g() = - ) Solve. ) In a lab eperiment grams of acid were produced in 9 minutes and 7 grams in minutes. Let be the grams produced in minutes. A) = + B) = + C) = - 89 D) = + 89 ) 8

9 Given the equation or other information for a parabola, find the matching description or graph. ) f() = a + b + c, a < 0; b - ac < 0 A) B) ) C) D) Use snthetic division to perform the division. 6) - - A) C) B) + + D) ) Epress the polnomial in the form P() = (- k)q() + r for the given value of k. 7) P() = ; k = - A) P() = ( + ) ( - + 6) + 0 B) P() = (- ) ( + ) + 6 C)P() = ( + ) ( + ) + 6 D) P() = ( + ) ( - + ) + 8 7) For the polnomial, one zero is given. Find all others. 8) P() = ; A) + i, - i B) + i, - i C) +, - D) - + i, - - i 8) Give all possible rational zeros for the following polnomial. 9) P() = A) ±, ±/, ±, ±, ±6, ±9, ±8 B) ±, ±, ±/, ±/, ±/6, ±/9, ±/8 C)±, ±, ±, ±6, ±9, ±8 D) ±, ±/, ±, ±, ±/, ±6, ±9, ±9/, ±8 9) 9

10 Find all rational zeros and factor f(). 0) f() = A), 8, -; f() = (- )( - 8)( +) B) -,-8, ; f() = ( + )( + 8)( - ) C) -,-7, ; f() = ( + )( + 7)( - ) D), 7, -; f() = (- )( - 7)( + ) 0) Find the zeros of the polnomial function and state the multiplicit of each. ) f() = ( + 9)( - 9) A), multiplicit ; 9, multiplicit ; -9, multiplicit B) -9, multiplicit ; 9, multiplicit C), multiplicit ; -9, multiplicit ; 9, multiplicit D) -9, multiplicit ; 9, multiplicit ) Find a polnomial of degree with real coefficients that satisfies the given conditions. ) Zeros of -,, 0 and P() = 6 A) P() = + - B) P() = + - C)P() = - - D) P() = ) Find a polnomial of lowest degree with onl real coefficients and having the given zeros. ) + i, A) f() = B) f() = C)f() = - - ( - i) + + 6i D) f() = ) Use Descartes' Rule of Signs to determine the possible number of positive real zeros and the possible number of negative real zeros for the function. ) = 0 A) Positive (), negative (0) B) Positive (0), negative (0) C) Positive (0), negative () D) Positive (), negative () ) 0

11 Sketch the graph of the rational function. ) f() = (- )( + ) ) A) B) C) D)

12 Use the graph to answer the question. 6) Find the horizontal and vertical asmptotes of the rational function graphed below. 6) A) Horizontal: none; vertical: = ± B) Horizontal: = -; vertical: = ± C)Horizontal: = 0; vertical: = ± D) Horizontal: = ±; vertical: = - Give the domain and range for the rational function. Use interval notation. 7) f() = (- ) + A) Domain: (-, -) (-, ); Range: (-, ) B) Domain: (-, ) (, ); Range: (-, 0) (0, ) C)Domain: (-, ) (, ); Range: (, ) D) Domain: (-, ) (, ); Range: (0, ) 7) Answer the question 8) How can the graph of f() = be obtained from the graph of =? A) B making a horizontal shift of 7 units to the left and a vertical shift of units down B) B making a horizontal shift of 7 units to the right and a vertical shift of units up C)B making a horizontal shift of units to the left and a vertical shift of 7 units up uupdown D) B making a horizontal shift of units to the right and a vertical shift of 7 units up 8) Determine which of the rational functions given below has the following feature(s). 9) -intercepts: - and -, -intercepts:, vertical asmptote: =, horizontal asmptote: = 9) A) f() = C)f() = ( + )( + ) ( - ) ( - )( - ) ( + ) B) f() = D) f() = ( - )( - ) ( + ) ( + )( + ) ( - ) Give the equation of the oblique asmptote, if an. 0) f() = A) = + 7 B) = + C) = + 7 D) None 0)

13 Write the partial fraction decomposition of the rational epression. - ) (- )( - ) A) B) C) D) ) Write the form of the partial fraction decomposition of the rational epression. It is not necessar to solve for the constants. - ) ) ( + )( + 7) A) C) A + + B C D ( + 7) A + + B C ( + 7) B) D) A + + B C D + E ( + 7) A + + B C + D ( + 7)

14 Answer Ke Testname: PRECALCULUS - EXAM REVIEW - FALL 00 ) A ) A ) C ) D ) B 6) A 7) A 8) B 9) D 0) B ) C ) D ) B ) A ) C 6) C 7) D 8) C 9) D 0) D ) A ) C ) C ) C ) C 6) B 7) A 8) A 9) D 0) D ) B ) A ) A ) B ) C 6) B 7) C 8) D 9) A 0) A ) C ) C