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1 Berkele Cit College Practice Problems Math 1 Precalculus - Final Eam Preparation Name Please print our name as it appears on the class roster. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. List the intercepts for the graph of the equation. 1) + = 1) Objective: (1.) Find Intercepts from an Equation ) = ) Objective: (1.) Find Intercepts from an Equation Write the standard form of the equation of the circle. ) ) (, ) (7, ) Objective: (1.) Write the Standard Form of the Equation of a Circle Write the standard form of the equation of the circle with radius r and center (h, k). ) r = 6; (h, k) = (, -) ) Objective: (1.) Write the Standard Form of the Equation of a Circle Find the center (h, k) and radius r of the circle with the given equation. ) ( + 6) + ( + ) = 0 ) Objective: (1.) Write the Standard Form of the Equation of a Circle Find the value for the function. 6) Find f( - 1) when f() = ) Objective: (.1) Find the Value of a Function Instructor: K Pernell 1

2 7) Find f( + 1) when f() = ) Objective: (.1) Find the Value of a Function Find the domain of the function. 8) g() = - 8) Objective: (.1) Find the Domain of a Function Defined b an Equation 9) h() = ) Objective: (.1) Find the Domain of a Function Defined b an Equation ) f() = 1 - ) Objective: (.1) Find the Domain of a Function Defined b an Equation For the given functions f and g, find the requested function and state its domain. 11) f() = 7 - ; g() = 9-9 Find f g. Objective: (.1) Form the Sum, Difference, Product, and Quotient of Two Functions 11) Solve the problem. 1) Find (fg)() when f() = - and g() = ) Objective: (.1) Form the Sum, Difference, Product, and Quotient of Two Functions 1) Find f g (-) when f() = - and g() = ) Objective: (.1) Form the Sum, Difference, Product, and Quotient of Two Functions Find and simplif the difference quotient of f, f( + h) - f(), h 0, for the function. h 1) f() = 1) Objective: (.1) Form the Sum, Difference, Product, and Quotient of Two Functions

3 The graph of a function f is given. Use the graph to answer the question. 1) For what numbers is f() > 0? 1) Objective: (.) Obtain Information from or about the Graph of a Function 16) How often does the line = 1 intersect the graph? 16) - - Objective: (.) Obtain Information from or about the Graph of a Function Answer the question about the given function. 17) Given the function f() = + + 8, is the point (-1, ) on the graph of f? 17) Objective: (.) Obtain Information from or about the Graph of a Function 18) Given the function f() = + 8-6, is the point (-, ) on the graph of f? 18) Objective: (.) Obtain Information from or about the Graph of a Function Find the average rate of change for the function between the given values. 19) f() = + 7; from 1 to 19) Objective: (.) Find the Average Rate of Change of a Function Write the equation of a sine function that has the given characteristics. 0) The graph of =, shifted 6 units upward 0) Objective: (.) Graph Functions Using Vertical and Horizontal Shifts 1) The graph of =, shifted 7 units to the right 1) Objective: (.) Graph Functions Using Vertical and Horizontal Shifts

4 Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. ) f() = ( - ) - ) - - Objective: (.) Graph Functions Using Vertical and Horizontal Shifts ) f() = ( + 6) + 7 ) - - Objective: (.) Graph Functions Using Vertical and Horizontal Shifts Use the accompaning graph of = f() to sketch the graph of the indicated equation. ) = - f( + ) + = f() ) Objective: (.) Graph Functions Using Compressions and Stretches

5 Determine the slope and -intercept of the function. ) h() = - - ) Objective: (.1) Graph Linear Functions Use the slope and -intercept to graph the linear function. 6) g() = ) - - Objective: (.1) Graph Linear Functions Find the verte and ais of smmetr of the graph of the function. 7) f() = ) Objective: (.) Identif the Verte and Ais of Smmetr of a Quadratic Function Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. 8) f() = + - 8) Objective: (.) Find the Maimum or Minimum Value of a Quadratic Function 9) f() = ) Objective: (.) Find the Maimum or Minimum Value of a Quadratic Function Solve the problem. 0) You have 0 feet of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maimize the enclosed area. Objective: (.) Find the Maimum or Minimum Value of a Quadratic Function 0) 1) You have feet of fencing to enclose a rectangular region. What is the maimum area? 1) Objective: (.) Find the Maimum or Minimum Value of a Quadratic Function ) The quadratic function f() = models the median, or average, age,, at which U.S. men were first married ears after In which ear was this average age at a minimum? (Round to the nearest ear.) What was the average age at first marriage for that ear? (Round to the nearest tenth.) Objective: (.) Find the Maimum or Minimum Value of a Quadratic Function )

6 Use the figure to solve the inequalit. ) f() < 0 16 ) 1 8 (-, 0) (, 0) Objective: (.) Solve Inequalities Involving a Quadratic Function Solve the inequalit. ) ) Objective: (.) Solve Inequalities Involving a Quadratic Function ) ) Objective: (.) Solve Inequalities Involving a Quadratic Function Form a polnomial whose zeros and degree are given. 6) Zeros: -, -, ; degree 6) Objective: (.1) Identif the Real Zeros of a Polnomial Function and Their Multiplicit 7) Zeros: -, -, -1, 1; degree 7) Objective: (.1) Identif the Real Zeros of a Polnomial Function and Their Multiplicit For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 8) f() = ( - 7)( + ) 8) Objective: (.1) Identif the Real Zeros of a Polnomial Function and Their Multiplicit 9) f() = ( + )( + ) 9) Objective: (.1) Identif the Real Zeros of a Polnomial Function and Their Multiplicit 0) f() = 1 ( - ) 0) Objective: (.1) Identif the Real Zeros of a Polnomial Function and Their Multiplicit Find the - and -intercepts of f. 1) f() = ( + 1)( - 6)( - 1) 1) Objective: (.1) Analze the Graph of a Polnomial Function 6

7 ) f() = - ( + 6)( + 1) ) Objective: (.1) Analze the Graph of a Polnomial Function Find the power function that the graph of f resembles for large values of. ) f() = 7 - ) Objective: (.1) Analze the Graph of a Polnomial Function Find the vertical asmptotes of the rational function. ) f() = ( - )( - 8) ) Objective: (.) Find the Vertical Asmptotes of a Rational Function ) f() = ) Objective: (.) Find the Vertical Asmptotes of a Rational Function Give the equation of the horizontal asmptote, if an, of the function. 6) h() = ) Objective: (.) Find the Horizontal or Oblique Asmptotes of a Rational Function 7) h() = ) Objective: (.) Find the Horizontal or Oblique Asmptotes of a Rational Function 8) g() = ) Objective: (.) Find the Horizontal or Oblique Asmptotes of a Rational Function Find the indicated intercept(s) of the graph of the function. 9) -intercept of f() = ( - 1)( - ) ) Objective: (.) Analze the Graph of a Rational Function 0) -intercepts of f() = ( - )( + 9) + - 0) Objective: (.) Analze the Graph of a Rational Function 7

8 Graph the function. 1) f() = ( - )( - ) 0 1) Objective: (.) Analze the Graph of a Rational Function ) f() = ) Objective: (.) Analze the Graph of a Rational Function Solve the inequalit. ) + < 0 ) Objective: (.) Solve Polnomial Inequalities ) < 0 ) Objective: (.) Solve Rational Inequalities ) + 18 < 9 ) Objective: (.) Solve Rational Inequalities 8

9 6) 8 7-6) Objective: (.) Solve Rational Inequalities Use the Rational Zeros Theorem to find all the real zeros of the polnomial function. Use the zeros to factor f over the real numbers. 7) f() = - - 7) Objective: (.) Find the Real Zeros of a Polnomial Function 8) f() = ) Objective: (.) Find the Real Zeros of a Polnomial Function 9) f() = ) Objective: (.) Find the Real Zeros of a Polnomial Function Find the intercepts of the function f(). 60) f() = ) Objective: (.) Find the Real Zeros of a Polnomial Function 61) f() = - ( + 6)( + 1) 61) Objective: (.) Find the Real Zeros of a Polnomial Function Information is given about a polnomial f() whose coefficients are real numbers. Find the remaining zeros of f. 6) Degree ; zeros: - i, 8i 6) Objective: (.6) Use the Conjugate Pairs Theorem Form a polnomial f() with real coefficients having the given degree and zeros. 6) Degree: ; zeros: - and + i. 6) Objective: (.6) Find a Polnomial Function with Specified Zeros 6) Degree: ; zeros: -1,, and 1 - i. 6) Objective: (.6) Find a Polnomial Function with Specified Zeros For the given functions f and g, find the requested composite function value. 6) f() = +, g() = ; Find (f g)(0). 6) Objective: (.1) Form a Composite Function 66) f() = +, g() = + 1; Find (g g)(1). 66) Objective: (.1) Form a Composite Function 67) f() = + 7, g() = -/; Find (g f)(). 67) Objective: (.1) Form a Composite Function For the given functions f and g, find the requested composite function. 68) f() = 7 + 6, g() = - 1; Find (f g)(). 68) Objective: (.1) Form a Composite Function 9

10 69) f() = - 1, g() = 8 ; Find (f g)(). 69) Objective: (.1) Form a Composite Function 70) f() = +, g() = 8-8; Find (f g)(). 70) Objective: (.1) Form a Composite Function Indicate whether the function is one-to-one. 71) {(, -), (6, -), (7, -7), (8, 9)} 71) Objective: (.) Determine Whether a Function Is One-to-One 7) {(, ), (-, -), (8, -), (-8, )} 7) Objective: (.) Determine Whether a Function Is One-to-One Decide whether or not the functions are inverses of each other. 7) f() = 8 -, g() = + 8 7) Objective: (.) Find the Inverse of a Function Defined b an Equation 7) f() = -, g() = ) Objective: (.) Find the Inverse of a Function Defined b an Equation 7) f() = + 1, g() = - 1 7) Objective: (.) Find the Inverse of a Function Defined b an Equation The function f is one-to-one. Find its inverse. 76) f() = +, 0 76) Objective: (.) Find the Inverse of a Function Defined b an Equation 77) f() = ) Objective: (.) Find the Inverse of a Function Defined b an Equation 78) f() = ) Objective: (.) Find the Inverse of a Function Defined b an Equation Solve the equation. 79) 7 - = 1 79) Objective: (.) Solve Eponential Equations

11 80) - = 6 80) Objective: (.) Solve Eponential Equations Change the eponential epression to an equivalent epression involving a logarithm. 81) 7 = 81) Objective: (.) Change Eponential Statements to Logarithmic Statements & Logarithmic Statements to Eponential Statements 8) = 8) Objective: (.) Change Eponential Statements to Logarithmic Statements & Logarithmic Statements to Eponential Statements Change the logarithmic epression to an equivalent epression involving an eponent. 8) log 1 = - 8) 8 Objective: (.) Change Eponential Statements to Logarithmic Statements & Logarithmic Statements to Eponential Statements 8) ln = 8) Objective: (.) Change Eponential Statements to Logarithmic Statements & Logarithmic Statements to Eponential Statements 8) ln 1 = - 8) e Objective: (.) Change Eponential Statements to Logarithmic Statements & Logarithmic Statements to Eponential Statements Find the eact value of the logarithmic epression. 86) log ) Objective: (.) Evaluate Logarithmic Epressions 87) log 87) Objective: (.) Evaluate Logarithmic Epressions Solve the equation. 88) log ( - ) = 1 88) Objective: (.) Solve Logarithmic Equations 89) ln = 89) Objective: (.) Solve Logarithmic Equations 90) ln + = 90) Objective: (.) Solve Logarithmic Equations 11

12 91) e + 7 = 91) Objective: (.) Solve Logarithmic Equations Write as the sum and/or difference of logarithms. Epress powers as factors. 9) log 8 9) Objective: (.) Write a Logarithmic Epression as a Sum or Difference of Logarithms 7 9) log 16 q p 9) Objective: (.) Write a Logarithmic Epression as a Sum or Difference of Logarithms 9) log mn 19 9) Objective: (.) Write a Logarithmic Epression as a Sum or Difference of Logarithms Epress as a single logarithm. 9) loga ( + 1) - loga ( - 1) + 9) Objective: (.) Write a Logarithmic Epression as a Single Logarithm Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round our answer to two decimal places. 96) log ) Objective: (.) Evaluate Logarithms Whose Base Is Neither Nor e Solve the equation. 97) log ( + ) - log ( - ) = log 97) Objective: (.6) Solve Logarithmic Equations 98) log + log( - ) = 98) Objective: (.6) Solve Logarithmic Equations Solve the equation. Epress irrational answers in eact form and as a decimal rounded to decimal places. 99) = 1-99) Objective: (.6) Solve Eponential Equations Convert the angle in degrees to radians. Epress the answer as multiple of!. 0) 1 0) Objective: (6.1) Convert from Degrees to Radians and from Radians to Degrees 1) 87 1) Objective: (6.1) Convert from Degrees to Radians and from Radians to Degrees 1

13 Convert the angle in radians to degrees. ) - 11! 6 ) Objective: (6.1) Convert from Degrees to Radians and from Radians to Degrees ) 9! ) Objective: (6.1) Convert from Degrees to Radians and from Radians to Degrees Find the eact value. Do not use a calculator. ) cos! ) Objective: (6.) Find the Eact Values of the Trigonometric Functions of Quadrantal Angles ) tan (19!) ) Objective: (6.) Find the Eact Values of the Trigonometric Functions of Quadrantal Angles 6) cos 16! 6) Objective: (6.) Find the Eact Values for Integer Multiples of!/6 = 0,!/ =, and!/ = 60 7) sec 19! 7) Objective: (6.) Find the Eact Values for Integer Multiples of!/6 = 0,!/ =, and!/ = 60 Find the eact value of the epression. Do not use a calculator. 8) tan 7! + tan! 8) Objective: (6.) Find the Eact Values for Integer Multiples of!/6 = 0,!/ =, and!/ = 60 9) sin 1 - sin 70 9) Objective: (6.) Find the Eact Values for Integer Multiples of!/6 = 0,!/ =, and!/ = 60 1) tan cos 1) Objective: (6.) Find the Eact Values for Integer Multiples of!/6 = 0,!/ =, and!/ = 60 Name the quadrant in which the angle θ lies. 111) cot θ < 0, cos θ > 0 111) Objective: (6.) Determine the Signs of the Trigonometric Functions in a Given Quadrant In the problem, sin θ and cos θ are given. Find the eact value of the indicated trigonometric function. 11) sin θ = 1, cos θ = 1 Find cot θ. 11) Objective: (6.) Find the Values of the Trigonometric Functions Using Fundamental Identities 1

14 Find the eact value of the indicated trigonometric function of θ. 11) tan θ = - 8, θ in quadrant II Find cos θ. 11) Objective: (6.) Find Eact Values of the Trig Functions of an Angle Given One of the Functions and the Quadrant of the Angle Without graphing the function, determine its amplitude or period as requested. 11) = - sin 1 Find the amplitude. 11) Objective: (6.) Determine the Amplitude and Period of Sinusoidal Functions 11) = - cos 1 Find the period. 11) Objective: (6.) Determine the Amplitude and Period of Sinusoidal Functions Match the given function to its graph. 116) 1) = sin ) = cos ) = sin ) = cos A B 116) 1 1 -π -π π π -1 -π -π π π C D 1 1 -π -π π π -1 -π -π π π Objective: (6.) Graph Sinusoidal Functions Using Ke Points 1

15 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Answer the question. 117) Which one of the equations below matches the graph? 117) A) = cos B) = cos 1 C) = sin 1 D) = cos 1 Objective: (6.) Graph Sinusoidal Functions Using Ke Points 118) Which one of the equations below matches the graph? 118) A) = cos B) = sin 1 C) = - sin 1 D) = cos 1 Objective: (6.) Graph Sinusoidal Functions Using Ke Points SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 119) What is the -intercept of = csc? 119) Objective: (6.) Graph Functions of the Form = A tan(ω) + B and = A cot(ω) + B Find the eact value of the epression. ) cos -1 ) Objective: (7.1) Find the Eact Value of an Inverse Sine, Cosine, or Tangent Function 1

16 11) cos -1-11) Objective: (7.1) Find the Eact Value of an Inverse Sine, Cosine, or Tangent Function Find the inverse function f -1 of the function f. 1) f() = cos + 6 1) Objective: (7.1) Find the Inverse Function of a Trigonometric Function 1) f() = tan( - ) 1) Objective: (7.1) Find the Inverse Function of a Trigonometric Function Find the eact solution of the equation. 1) cos -1 =! 1) Objective: (7.1) Solve Equations Involving Inverse Trigonometric Functions Find the eact value of the epression. 1) cos sin ) Objective: (7.) Find the Eact Value of Epressions Involving the Inverse Sine, Cosine, and Tangent Functions 16) sec sin ) Objective: (7.) Find the Eact Value of Epressions Involving the Inverse Sine, Cosine, and Tangent Functions Solve the equation on the interval 0 θ < ". 17) cos θ + = 17) Objective: (7.) Solve Equations Involving a Single Trigonometric Function Solve the equation. Give a general formula for all the solutions. 18) sin θ = 1 18) Objective: (7.) Solve Equations Involving a Single Trigonometric Function Solve the equation on the interval 0 θ < ". 19) cos θ + cos θ + 1 = 0 19) Objective: (7.) Solve Trigonometric Equations Quadratic in Form ) sin θ = sin θ ) Objective: (7.) Solve Trigonometric Equations Quadratic in Form Simplif the trigonometric epression b following the indicated direction. 11) Rewrite in terms of sine and cosine: tan cot 11) Objective: (7.) Use Algebra to Simplif Trigonometric Epressions 16

17 1) Multipl sin θ b 1 + cos θ 1 - cos θ 1 + cos θ 1) Objective: (7.) Use Algebra to Simplif Trigonometric Epressions The polar coordinates of a point are given. Find the rectangular coordinates of the point. 1) 7,! 1) Objective: (9.1) Convert from Polar Coordinates to Rectangular Coordinates 1) -,! 1) Objective: (9.1) Convert from Polar Coordinates to Rectangular Coordinates The rectangular coordinates of a point are given. Find polar coordinates for the point. 1) (0, -8) 1) Objective: (9.1) Convert from Rectangular Coordinates to Polar Coordinates 16) (-, -1) 16) Objective: (9.1) Convert from Rectangular Coordinates to Polar Coordinates The letters and represent rectangular coordinates. Write the equation using polar coordinates (r, θ). 17) + = 17) Objective: (9.1) Transform Equations between Polar and Rectangular Forms 18) = 16 18) Objective: (9.1) Transform Equations between Polar and Rectangular Forms Transform the polar equation to an equation in rectangular coordinates. Then identif and graph the equation. 19) r = 19) r Objective: (9.) Identif and Graph Polar Equations b Converting to Rectangular Equations 17

18 ) r = sin θ ) r Objective: (9.) Identif and Graph Polar Equations b Converting to Rectangular Equations 11) r sin θ = 11) r Objective: (9.) Identif and Graph Polar Equations b Converting to Rectangular Equations Write the comple number in polar form. Epress the argument in degrees, rounded to the nearest tenth, if necessar. 1) + i 1) Objective: (9.) Convert a Comple Number between Rectangular Form and Polar Form 1) + i 1) Objective: (9.) Convert a Comple Number between Rectangular Form and Polar Form Find zw or z w as specified. Leave our answer in polar form. 1) z = 8 cos! 6 + i sin! 6 1) w = cos! + i sin! Find zw. Objective: (9.) Find Products and Quotients of Comple Numbers in Polar Form 18

19 1) z = (cos + i sin ) w = (cos 1 + i sin 1 ) 1) Find z w. Objective: (9.) Find Products and Quotients of Comple Numbers in Polar Form Write the epression in the standard form a + bi. 16) (cos 1 + i sin 1 ) 16) Objective: (9.) Use De Moivre's Theorem 17) (- + i) 6 17) Objective: (9.) Use De Moivre's Theorem MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the equation to the graph. 18) ( + ) = 8( + 1) A) B) 18) C) D) Objective: (.) Analze Parabolas with Verte at (h, k) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find an equation for the parabola described. 19) Verte at (8, 7); focus at (8, ) 19) Objective: (.) Analze Parabolas with Verte at (h, k) 19

20 Write an equation for the graph. ) ) - (, -1) - Objective: (.) Analze Ellipses with Center at (h, k) Find the center, foci, and vertices of the ellipse. 11) = 0 11) Objective: (.) Analze Ellipses with Center at (h, k) Graph the equation. 1) ( + 1) 9 + ( - ) = 1 1) - - Objective: (.) Analze Ellipses with Center at (h, k) Find an equation for the hperbola described. 1) center at (, ); focus at (0, ); verte at (1, ) 1) Objective: (.) Analze Hperbolas with Center at (h, k) Find the center, transverse ais, vertices, foci, and asmptotes of the hperbola. 1) = 0 1) Objective: (.) Analze Hperbolas with Center at (h, k) 0

21 Graph the hperbola. 1) ( + ) - ( - ) 9 = 1 1) - - Objective: (.) Analze Hperbolas with Center at (h, k) Solve the sstem of equations b substitution. 16) - = -1 + = Objective: (11.1) Solve Sstems of Equations b Substitution 16) Solve the sstem of equations. 17) - + z = z = z = - Objective: (11.1) Solve Sstems of Three Equations Containing Three Variables 17) Perform the row operation(s) on the given augmented matri. 18) R = -r1 + r 1-8 Objective: (11.) Perform Row Operations on a Matri 19) (a) R = -r1 + r (b) R = -r1 + r (c) R = 6r + r ) 19) Objective: (11.) Perform Row Operations on a Matri Write the partial fraction decomposition of the rational epression. 160) ( - )( - ) 160) Objective: (11.) Decompose P/Q, Where Q Has Onl Nonrepeated Linear Factors 1

22 + 161) ) Objective: (11.) Decompose P/Q, Where Q Has Repeated Linear Factors 16) + ( - 1)( + + 1) Objective: (11.) Decompose P/Q, Where Q Has a Nonrepeated Irreducible Quadratic Factor 16) Graph the equations of the sstem. Then solve the sstem to find the points of intersection. 16) = = ) - - Objective: (11.6) Solve a Sstem of Nonlinear Equations Using Substitution Solve the sstem of equations using substitution. 16) 16) + = + = -7 Objective: (11.6) Solve a Sstem of Nonlinear Equations Using Substitution ln = ln = 7 Objective: (11.6) Solve a Sstem of Nonlinear Equations Using Substitution 16) 16) Solve using elimination. 166) + = 1 - = 17 Objective: (11.6) Solve a Sstem of Nonlinear Equations Using Elimination 166)

23 167) + = 17 - = -6 Objective: (11.6) Solve a Sstem of Nonlinear Equations Using Elimination 167)

24 Answer Ke Testname: MATH1_FINAL_EXAM_PRACTICE 1) (-1, 0), (0, -), (0, ), (1, 0) ) (-, 0), (-8, 0), (0, 0) ) ( - ) + ( - ) = ) ) ( - ) + ( + ) = 6 ) (h, k) = (-6, -); r = 6 6) ) ) { -, } 9) { -9, 0, 9} ) { 1} 11) (f g)() = ; all real numbers 1) -6 ) - - 1) 1) (+h) 1) [0, -60), (70, 0) 16) three times 17) Yes 18) No 19) ) = + 6 1) = - 7 ) ) m = -; b = - 6) ) (-, 1) ; = - 8) minimum; - 9) maimum; - 0) ft b ft 1) 661 square feet ) 199,.6 ears old ) { - < < }; (-, ) ) (-, 0] or [8, ) ) [-8, 8] 6) f() = for a = 1

25 Answer Ke Testname: MATH1_FINAL_EXAM_PRACTICE 7) ) 7, multiplicit 1, crosses -ais; -, multiplicit, crosses -ais 9) -, multiplicit, touches -ais 0) 0, multiplicit 1, crosses -ais;, multiplicit 1, crosses -ais; -, multiplicit 1, crosses -ais 1) -intercepts: -1, 1, 6; -intercept: -6 ) -intercepts: -6, 0; -intercept: 0 ) = - ) =, = 8 ) = 0, = - 6) = 8 7) no horizontal asmptotes 8) = 0 9) 0, - 19 ) -, ) (-9, 7) ) (-, 0) or (, 6) 6) (-, 0] or [, 7) 7) -, ; f() = ( - )( + )( + 1) 8) -, -, ; f() = ( + )( + )( - ) 9) ; f() = ( - )( + ) 60) -intercepts: -, -1, ; -intercept: -6 61) -intercepts: -6, 0; -intercept: 0 6) + i, -8i 6) f() = ) f() = ) 66) 19 67) - 1 0) (, 0), - 9, 0 1) ) ) ) 8-70) ) No 7) Yes 7) No 7) Yes 7) Yes; Eclude the interval (-, 1) 76) f -1 () = -, 77) f -1 () = ) f -1 () = ) {} 80) {, -} 81) log 7 = 8) log = 8) - = 1 8 8) e = 8) e - = 1 e 86) - 87) 1 88) {, -1}

26 Answer Ke Testname: MATH1_FINAL_EXAM_PRACTICE 89) {e -1/ } 90) {e 6 - } 91) {ln - 7} 9) log - 8 log 9) 1 7 log 16 - log q - log p 9) 1 log m + 1 log n - 1 log 19 9) loga a ( + 1) ( - 1) 96) ) {9} 98) {7} ln 99) ln + ln 0.8 0)! 1) 9! 60 ) -0 ) 680 ) 1 ) 0 6) - 1 7) - 8) 0 9) + 1) ) IV 11) 1 11) ) 11) 8! 116) 1B, D, C, A 117) A 118) B 119) none 11)! 6 1) f -1 () = cos ) f -1 () = 1 tan-1 + 1) 1) 16) )!,! 18) θ θ =! + k! 19) {!} ) 0,!,! 6,! 6 11) 1 1) 1 + cos θ sin θ 1) - 7, 7 1) 1) 8, -! 16), -! 6, - 17) r (cos θ + sin θ) = 18) r sin θ = 16 cos θ )! 6 6

27 Answer Ke Testname: MATH1_FINAL_EXAM_PRACTICE 19) = ; circle, radius, center at pole r 1) (cos 0 + i sin 0 ) 16) + i 17) -6 18) D 19) ( - 8) = -16( - 7) ) 11) 1) ( - ) 16 ( - 6) + + ( + 1) 9 ( + ) = 1 = 1 center: (6, -); foci: (7, -), (, -); vertices: (8, -), (, -) ) ( - 1) = 1; circle, radius 1, center at (0, 1) in rectangular coordinates 11) 1 r - 1) ( - ) - - ( - ) = 1 1) center at (-, 1) transverse ais is parallel to -ais vertices at (-8, 1) and (, 1) 1) foci at (- - 6, 1) and (- + 6, 1) asmptotes of - 1 = - 1 ( + ) and - 1 = 1 ( + ) = ; horizontal line units above the pole 1) (cos 0 + i sin 0 ) 1) (cos + i sin ) 1) cos! + i sin! r ) =, = 8; (, 8) 17) = 0, = 1, z = -; (0, 1, -) 18)

28 Answer Ke Testname: MATH1_FINAL_EXAM_PRACTICE 19) 160) ) ( - 1) 16) 16) (, ), (, 1) 16) = -, = -; = -, = - or (-, -), (-, -) 16) =, = or (, ) 166) = 9, = 8; = -9, = 8; = 9, = -8; = -9, = -8 or (9, 8), (-9, 8), (9, -8), (-9, -8) 167) =, = ; =, = -; = -, = ; = -, = - or (, ), (, -), (-, ), (-, -) 8

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