College Algebra Final Exam Review. 5.) State the domain of the following functions. Then determine whether each function is a one-toone function.

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1 College Algebra Final Eam Review For # use the given graph f():.) Find f( )..) State the zeros, the domain, and the range. f().) State the local maimum and/or minimum..) State the intervals decreasing and increasing ) State the domain of the following functions. Then determine whether each function is a one-toone function. a) f() = 5 Is this function one-to-one? b) f() = + +0 Is this function one-to-one? c) f() = + Is this function one-to-one? d) f() = e Is this function one-to-one? e) f() = ln( +) Is this function one-to-one? ) Find the difference quotient 7.) Find the difference quotient f( f( h) f() h h) f() h for f() =. for f() = ) If the square root function is shifted 6 units to the right and units down, what is the resulting function? State the domain. 9.) If the function f() = is shifted 7 units up and units to the left, what is the resulting function? State the domain. 0.) For the function of f() shown below, use transformations to sketch the graph of f( )..) Graph f() b appling transformations to f(). Give the equations of the asmptotes.

2 College Algebra Final Eam Review page.) Determine algebraicall if the following functions are even, odd, or neither. a) f() = b) g() = 5 + c) h() = ) Let f() = 9 and g() = +. Simplif completel. a) Find (f + g)() b) Find (f g)() c) Find (fg)() d) Find (f/g)() e) Find (f g)().) Find the verte, -intercept, and -intercepts, if the eist, for f() = 5. 5.) Solve = 0. 6.) P() = is a profit function where is the number of items sold, and P() is the profit from that sale. Find the maimum profit and the number of items that must be sold to reach that profit. 7.) Analze the polnomial f() = 7( ) ( + ) ( + ) and complete the chart below. zeros multiplicit (how man times it occurs) Does the graph touch or cross at this intercept? State the degree of the polnomial function. Determine the end behavior of the graph of the function. 8.) When a person gets a single flu shot, the concentration of the drug in milligrams per liter after t hours in the bloodstream is modeled b the following equation. Find the horizontal asmptote of the function, F(t), and interpret what the horizontal asmptote represents with respect to the concentration of flu medication in the bloodstream as time passes. F(t) 7.6t t ) For the rational function R() find the domain (D), equation of the vertical asmptote (VA), and equation of the horizontal asmptote (HA), if it eists. If non-eistent, write NONE. 0.) Find all of the comple zeros for f() = 5 0. Also use the Rational Zeros Theorem to list the possible rational zeros..) Find all of the comple zeros for f() = Also use the Rational Zeros Theorem to list the possible rational zeros..) Find f( ) using Snthetic Division and the Remainder Theorem if f() = 5 0.

3 College Algebra Final Eam Review page.) Find a polnomial function that has as it zeros =, =, = i, = i. Write the polnomial function as a product of linear factors. 7.) The formula S = D can be used to approimate the speed S, in miles per hour, of a car that has left skid marks of length D, in feet. How far will a car skid at 70 mph? Round to one decimal place. 5.) The population P after t ears of a newl introduced species of wildcat can be modeled b the 900t 8000 equation P(t). t 000 a) Find the horizontal asmptote (HA). b) Interpret this asmptote: As time, t, increases, the number of wildcats will approach and level off at. 6.) Find f - () for f() = + and 8 g(). 7 7.) Write the following log epression as the sum and/or difference of logs with no eponents or radicals remaining: log. z 8.) Solve 6 + e = 9. 9.) Solve log (8) = 0. 0.) Solve log ( + ) log ( ) = log ()..) Solve: 6 = +..) Simplif: log 5 (5)..) Convert to a logarithmic equation: =.8..) Solve: log () + log ( + 7) =. 5.) Solve using Gauss-Jordan Elimination: z z z 6.) Ron attends a cocktail part. He wants to limit his food intake to g protein, 0 g fat, and 65 g carbohdrate. According to the health conscious hostess, the marinated mushroom caps have g protein, 5 g fat, and 9 g carbohdrate; the spic meatballs have g protein, 7 g fat, and 5 g carbohdrate; and the deviled eggs have g protein, 5 g fat, and 6 g carbohdrate. How man of each snack can he eat to obtain his goal? Solve using the Gauss-Jordan Elimination Method.

4 College Algebra Final Eam Review page 7.) If a couple needs $,500 for a down pament on a house and the invest the $0,800 the have at 5.8%, compounded continuousl, how long will it take for their mone to grow to the $,500 needed? 8.) A radioactive substance decas according to the model A(t) = A 0 e 0.007t, where A 0 is the initial amount present and t is the time in ears. a) If there are 0 grams present initiall, when will there be grams remaining? b) In how man ears will 80% of the original amount remain? 9.) For an arithmetic sequence with a = and d =, a) Find a b) Find a formula for the nth term. 0.) For the arithmetic sequence,, 5, 9,..., a) Find the common difference d b) Find a formula for the nth term d) Find a 5..) For the geometric sequence with a = and r =, a) Find a b) Find a formula for the nth term..) For the geometric sequence 0,,,,, 5 5 a) Find a b) Find a formula for the nth term..) Find the indicated sum of the arithmetic series: ( 5 n). n.) Find the indicated sum of the geometric series: 75 n. n 5.) If possible, find the sum of each geometric series: a) n n b) 5 n n. 6.) Consider the piecewise defined function a) Find f( ), f(), and f(5) + for < 0 f() =. + for b) Graph this function. 7.) State the domain (D), range (R), & equation of the horizontal asmptote (HA) for each function. + a) f() = e +5 b) g() = e - 5 c) h() = e 5. 8.) State the domain (D), range (R), & equation of the vertical asmptote (HA) for each function. a) f() = log( ) b) g() = ln( + ) c) h() = log()

5 College Algebra Final Eam Review page 5 9.) Which of the following graphs represents the graph of f() = + +? Which of the following graphs represents the graph of g() =? a) b) c) d) e) 50.) Write the resulting matri after the row operations have been applied: R + R R R R 5 5.) State the domain and range of each graph. Determine whether each function is a one-to-one function. a) b) c) d) e) f)

6 College Algebra Final Eam Review page 6 5.) Find the st terms of the sequence whose n th term is a n = n +. 5.) Find and evaluate: (k ). k 5.) Suppose that a polnomial function of degree 5 with rational coefficients has, i, and + i as zeros. Find the remaining zeros. 55.) Write as a single logarithm: log() + log() log(5) 56.) For each polnomial function graphed, determine the minimum possible degree, the zeros and if the multiplicit of the zeros is even or odd. a) b) Answers.).) 5, 0, ; Domain: (, ]; Range: [, ).) Local ma: when = Local min: when =.) Intervals decreasing: (, ) U (, ) Interval increasing: (, ) 5 5.) a), ; es b) (, ); no c),, ; es d) (, ); es e) (, ); es 6.) 7.) 6 + h + 8.) f() 6 ; Domain: [6, ) 9.) f() = ( + ) + 7; Domain: (, )

7 College Algebra Final Eam Review page 7 0.).) VA: = HA: =.) Recall the algebraic definitions of even & odd: g( ) = g() => g is even => smmetr about the -ais g( ) = g() => g is odd => smmetr about the origin a) Even: Show that f( ) = f() b) Odd: Show that g() = g( ) f() = g() = 5 + f( ) = ( ) ( ) = g( ) = ( ) 5 + ( ) = 5 g() = ( 5 + ) = 5 c) Neither: Show that h( ) does not equal h() and h( ) does not equal h() h() = h() = 7( ) + 5( ) = 7 5 h() = (7 + 5 ) = ) a) (f + g)() = 7 + b) (f g)() = c) (fg)() = 5 7 d) (f/g)() = 9 e) (f g)() = 6 8.) Verte: (, 6); -intercept: (0, 5); -intercepts: ( 5,0) and (7, 0) 5.) 6.) maimum profit: $75; number of items: 5 7.) zero: has a multiplicit of, crosses zero: has a multiplicit of, touches zero: has a multiplicit of crosses degree: 6 end behavior: up left and up right 8.) HA: = 0; As time passes (t increases), the concentration of flu medication in the bloodstream approaches ) D:,, ; VA: = ; HA: = 5 0.) zeros:,, 5 possible rational zeros:,, 5, 0,,.) zeros:,, + i, i possible rational zeros:,,, 5, 0, 0

8 College Algebra Final Eam Review page 8.) 0; snthetic division: 5 0 The remainder is 0, so f( ) = ) f() = ( + )( )( i)( + i).) 00 feet 5.) HA: = 00; 00 wildcats 6.) f () g - () = ) log () + ½log ( + ) log () log (z) 8.) = 9.) = 8 0.) = 7.) =.) = ln() 0.77.) = log (.8).) = 5.) Solution: (,, ); Set of Row Operations: R + R R R + R R R R 0 R + R R 8R + R R 5 R R 7 9 R + R R 0 7 R + R R 0 6.) # of mushrooms caps = 8 # of meatballs = 5 # of deviled eggs = 7) 5.08 ears 8.) a) in 08 ears b) in 7. ears

9 College Algebra Final Eam Review page 9 9.) a = 77; a n = n 5 0.) d = ; a n = n + 7; a 5 = n-.) a =,,5,7; a n = () n 6.) a =.00 ; a n = 0 5.) 6675.) 65 5.) a) b) The sum does not eist. 6.) a) f( ) = 5, f() is undefined, f(5) = 7 b) 7.) a) D: (, ); R: (5, ); HA: = 5 b) D: (, ); R: ( 5, ); HA: = 5 c) D: (, ); R: (, 5); HA: = 5 8.) a) D: (, ); R: (, ); VA: = b) D: (, ); R: (, ); VA: = c) D: (0, ); R: (, ); VA: = 0 9.) a); b) 50.) / ) a) (, ) b) (, ) c) (, ) d) (, ) e) [0, ) f) (, )U(, ) (, ] [, ) (, ) (, ) [, ) (, )U(, ) No No Yes Yes Yes Yes 5.), 5 0, 7 5.) 5.) i, i 55.) log 5 56.) a) Degree ; zeros: (odd multiplicit), 0 (odd multiplicit), (odd multiplicit) b) Degree: ; zeros: (odd multiplicit), 0 (odd multiplicit), (even multiplicit)