Name Period Date. Practice FINAL EXAM Intro to Calculus (50 points) Show all work on separate sheet of paper for full credit!


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1 Name Period Date Practice FINAL EXAM Intro to Calculus (0 points) Show all work on separate sheet of paper for full credit! ) Evaluate the algebraic epression for the given value or values of the variable(s). + (  ); = ) Evaluate the algebraic epression for the given value or values of the variable(s).  ; =  and = 7 + 0) Simplif the eponential epression.  ) Add or subtract terms whenever possible ) Add or subtract terms whenever possible ) Find the union of the two sets. {, 0,, 9} {,, } ) List all the irrational numbers numbers from the given set B that are members of the given real number subset. B = {9, 8, 9, 0,,, 0., 0.77} ) Rationalize the denominator. 97 ) Rationalize the denominator ) Evaluate the epression for the given values of and. + ; = and =  ) State the name of the propert illustrated. ( ) = ( ) 7) Evaluate the eponential epression. 7 8) Evaluate the eponential epression. () 9) Simplif the eponential epression. 99 z ) Add or subtract terms whenever possible ) Add or subtract terms whenever possible ) Simplif b reducing the inde of the radical. 8) Simplif b reducing the inde of the radical. 9 z 9) Perform the indicated operations. Write the resulting polnomial in standard form. ( )  ( ) 0) Find the product. ( + )( )
2 ) Find the product. (9  )(  + ) ) Find the product. ( + )(  ) ) Find the product. ( + ) ) Simplif the rational epression. Find all numbers that must be ecluded from the domain of the simplified rational epression ) Multipl or divide as indicated. (  7)  ) Factor.  ) Factor. (  )  (  ) ) Factor ) Factor the trinomial, or state that the trinomial is prime.  + ) Multipl or divide as indicated ) Multipl or divide as indicated ) Multipl or divide as indicated ) Factor completel, or state that the polnomial is prime ) Add or subtract as indicated ) Factor completel, or state that the polnomial is prime. + 9) Add or subtract as indicated ) Factor using the formula for the sum or difference of two cubes ) Add or subtract as indicated ) Factor using the formula for the sum or difference of two cubes. 8  ) Find all numbers that must be ecluded from the domain of the rational epression ) Simplif the comple rational epression.  +
3 ) Simplif the comple rational epression ) Solve the absolute value equation or indicate that the equation has no solution.  = 8 ) Solve the absolute value equation or indicate that the equation has no solution.   = 8 ) Solve the formula for the specified variable. a + b = for c c ) Solve the formula for the specified variable. A = h(b + b) for b 7) Solve the equation. + = ) Epress the interval in setbuilder notation and graph the interval on a number line. [, ] ) Use graphs to find the set. (8, 0) [, 0] ) Use graphs to find the set. (, ) [8, ) ) Solve the quadratic equation using the quadratic formula. = 8  ) Evaluate the function at the given value of the independent variable and simplif. f() = +  ; f() 7) Use the graph to determine the  and intercepts. 0 8) Solve the absolute value inequalit. Use interval notation to epress the solution set and graph the solution set on a number line.   < ) Solve the quadratic equation using the quadratic formula = ) Solve the compound inequalit. Use interval notation to epress the solution set and graph the solution set on a number line < 8 ) Epress the interval in setbuilder notation and graph the interval on a number line. [7, ) 8) Give the domain and range of the relation. {(, ), (, ), (0, ), (, ), (, 0)} 9) Determine whether the relation is a function. {(, 9), (, 8), (, ), (9, 8), (, 9)} 0) Determine whether the relation is a function. {(7, ), (, ), (, ), (, 7)}
4 ) Determine whether the equation defines as a function of. = ) Find the slope of the line that goes through the given points. (, 9), (, 8) ) Determine whether the equation defines as a function of. + 7 = 7) Find the slope of the line that goes through the given points. (, ) and (, ) ) Graph the given functions on the same rectangular coordinate sstem. Describe how the graph of g is related to the graph of f. f() =, g() =  8) Find the slope of the line that goes through the given points. (8, 7), (, 7) ) Use the graph to find the indicated function value. = f(). Find f() 9) Use the given conditions to write an equation for the line in pointslope form. Passing through (, ) and (7, ) ) Use the given conditions to write an equation for the line in pointslope form. Passing through (, 7) with intercept =  7) Determine the slope and the intercept of the graph of the equation = 0 7) Use the given conditions to write an equation for the line in slopeintercept form. Slope = 7, passing through (, ) 8 ) Use the graph to determine the function's domain and range. 7) Use the vertical line test to determine whether or not the graph is a graph in which is a function of
5 7) Use the given conditions to write an equation for the line in the indicated form. Passing through (, ) and perpendicular to the line whose equation is = + 7; slopeintercept form 7) Given functions f and g, determine the domain of f + g. f() = , g() = + 9 7) Find an equation for the line with the given properties. The solid line L contains the point (, ) and is perpendicular to the dotted line whose equation is =. Give the equation of line L in slopeintercept form. 80) Given functions f and g, perform the indicated operations. f() = +, g() =  Find fg. 8) Given functions f and g, perform the indicated operations. f() =  8, g() = Find f + g. 8) Given functions f and g, determine the domain of f + g. f() = , g() =  8) Find the domain of the indicated combined function. f Find the domain of g () when f() = 8  and g() = ) For the given functions f and g, find the indicated composition. f() = + +, g() =  (g f)()  77) Use the given conditions to write an equation for the line in the indicated form. Passing through (, ) and parallel to the line whose equation is = ; slopeintercept form 78) Begin b graphing the standard absolute value function f() =. Then use transformations of this graph to graph the given function. h() =  79) Begin b graphing the standard quadratic function f() =. Then use transformations of this graph to graph the given function. h() = ( + ) + 8) Find the domain of the function. g() =  8) Find the domain of the function. f() = 987) For the given functions f and g, find the indicated composition. f() =  +, g() = + (g f)() 88) Find the domain of the composite function f g. f() = + 7, g() = + 89) Find the domain of the composite function f g. f() = ; g() = +
6 90) Find functions f and g so that h() = (f g)(). h() = + 0 9) Find functions f and g so that h() = (f g)(). h() =  9) Determine which two functions are inverses of each other. f() =  g() =  h() = + 9) Determine which two functions are inverses of each other. f() = + g() = + h() =  9) Find the inverse of the onetoone function. f() = 89) Add or subtract as indicated and write the result in standard form.  ( + 9i)  (  7i) 00) Perform the indicated operations and write the result in standard form ) Perform the indicated operations and write the result in standard form. (  ) 0) Solve the quadratic equation using the quadratic formula. Epress the solution in standard form.  + = 0 0) Determine whether the given quadratic function has a minimum value or maimum value. Then find the coordinates of the minimum or maimum point. f() =  + 0) Determine whether the given quadratic function has a minimum value or maimum value. Then find the coordinates of the minimum or maimum point. f() =  + 9) Find the product and write the result in standard form. ( + i)(  i) 0) Use the verte and intercepts to sketch the graph of the quadratic function. + = ( + ) 97) Perform the indicated operations and write the result in standard form. ( + i)  (  i) 98) Divide and epress the result in standard form. i  i 99) Perform the indicated operations and write the result in standard form ) Find the zeros of the polnomial function. f() = ) Divide using long division. ( ) ( + ) 08) Divide using snthetic division. ( ) ( + ) 09) Divide using snthetic division
7 0) Graph the function b making a table of coordinates. f() = 0. ) Approimate the number using a calculator. Round our answer to three decimal places. e0. ) Find the accumulated value of an investment of $,000 at % compounded semiannuall for ears. 0) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. log 9  ) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. log b + 8log b z ) Suppose that ou have $0,000 to invest. Which investment ields the greater return over 7 ears: 8.7% compounded continuousl or 8.9% compounded semiannuall? ) Use the graph of f() = e to obtain the graph of g() = e . ) Write the equation in its equivalent logarithmic form. = ) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. log b m  log b n ) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. log 0,000 ) Write the equation in its equivalent eponential form. log = 7) Evaluate the epression without using a calculator. log 7 7 8) Evaluate the epression without using a calculator. log 9) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. log + 7
8 Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL ) ID: PCALCZ Objective: (0.) Evaluate Algebraic Epressions )  8 ID: PCALCZ Objective: (0.) Evaluate Algebraic Epressions ) {,, 9, 0, } ID: PCALCZ Objective: (0.) Find the Union of Two Sets ) 8 ID: PCALCZ Objective: (0.) Recognize Subsets of the Real Numbers ) 0 ID: PCALCZ Objective: (0.) Evaluate Absolute Value ) Commutative propert of multiplication ID: PCALCZ Objective: (0.) Identif Properties of the Real Numbers 7) ID: PCALCZ Objective: (0.) Use Properties of Eponents 8) ID: PCALCZ Objective: (0.) Use Properties of Eponents 9) 9z 9 0) ID: PCALCZ Objective: (0.) Simplif Eponential Epressions 79 ID: PCALCZ Objective: (0.) Simplif Eponential Epressions )  ID: PCALCZ Objective: (0.) Add and Subtract Square Roots )  ID: PCALCZ Objective: (0.) Add and Subtract Square Roots ) ID: PCALCZ Objective: (0.) Rationalize Denominators ) 07 ID: PCALCZ Objective: (0.) Rationalize Denominators ) 8 7 ID: PCALCZ Objective: (0.) Evaluate and Perform Operations with )  7 ID: PCALCZ Objective: (0.) Evaluate and Perform Operations with 7) ID: PCALCZ Objective: (0.) Understand and Use Rational Eponents 8) /7z/7 ID: PCALCZ Objective: (0.) Understand and Use Rational Eponents 9) ID: PCALCZ Objective: (0.) Add and Subtract Polnomials 0) ID: PCALCZ Objective: (0.) Multipl Polnomials ) ID: PCALCZ Objective: (0.) Multipl Polnomials )  ID: PCALCZ Objective: (0.) Use Special Products in Polnomial ) ID: PCALCZ Objective: (0.) Use Special Products in Polnomial ) ( + )(  ) ID: PCALCZ Objective: (0.) Factor the Difference of Squares ) (  )(  ) ID: PCALCZ Objective: (0.) Factor Out the Greatest Common Factor of ) (  )( + 8) ID: PCALCZ Objective: (0.) Factor b Grouping 7) (  )(  ) ID: PCALCZ Objective: (0.) Factor Trinomials 8) (  )( + )(  ) ID: PCALCZ Objective: (0.) Use a General Strateg for Factoring 9) ( + )(  + ) ID: PCALCZ Objective: (0.) Use a General Strateg for Factoring 8
9 Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL 0) ( + )(9  + ) ID: PCALCZ Objective: (0.) Factor the Sum and Difference of Two ) (  )( + + ) ID: PCALCZ Objective: (0.) Factor the Sum and Difference of Two ), ID: PCALCZ Objective: (0.) Specif Numbers That Must Be Ecluded ) +, ,  ID: PCALCZ Objective: (0.) Simplif Rational Epressions )  7 ID: PCALCZ Objective: (0.) Divide Rational Epressions ) ID: PCALCZ Objective: (0.) Divide Rational Epressions ) 8 7 ID: PCALCZ Objective: (0.) Multipl Rational Epressions 7) ) ID: PCALCZ Objective: (0.) Multipl Rational Epressions   ( + )(  ) ID: PCALCZ Objective: (0.) Add and Subtract Rational Epressions 9)   0)  ) ID: PCALCZ Objective: (0.) Add and Subtract Rational Epressions  8 ID: PCALCZ Objective: (0.) Add and Subtract Rational Epressions  + ID: PCALCZ Objective: (0.) Simplif Comple Rational Epressions ) 9 ID: PCALCZ Objective: (0.) Simplif Comple Rational Epressions ) {9, } ID: PCALCZ Objective: (0.7) Solve Equations Involving Absolute Value ) {,, } ID: PCALCZ Objective: (0.7) Solve Equations Involving Absolute Value ) c = ab a + b ID: PCALCZ Objective: (0.7) Solve a Formula for a Variable A  Bh ) b = h ID: PCALCZ Objective: (0.7) Solve a Formula for a Variable 7) {} ID: PCALCZ Objective: (0.7) Solve Rational Equations with Variables in 8) 9) ID: PCALCZ Objective: (0.9) Solve Absolute Value Inequalities , ID: PCALCZ Objective: (0.7) Solve Quadratic Equations Using the 0) (, ] ID: PCALCZ Objective: (0.9) Solve Compound Inequalities ) { 7} ID: PCALCZ Objective: (0.9) Use Interval Notation ) {  } ID: PCALCZ Objective: (0.9) Use Interval Notation ) [, 0) ID: PCALCZ Objective: (0.9) Find Intersections and Unions of Intervals 9
10 Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL ) (, ) ID: PCALCZ Objective: (0.9) Find Intersections and Unions of Intervals )  ,  + ID: PCALCZ Objective: (0.7) Solve Quadratic Equations Using the )  ID: PCALCZ..7+ Objective: (.) Evaluate a Function 7) intercepts: ,, ; intercept: ID: PCALCZ..+ Objective: (.) Use a Graph to Determine Intercepts 8) domain: {, , 0,, }; range: {,,, 0} ID: PCALCZ..7+ Objective: (.) Find the Domain and Range of a Relation 9) Not a function ID: PCALCZ..+ Objective: (.) Determine Whether a Relation is a 0) Function ID: PCALCZ..7+ Objective: (.) Determine Whether a Relation is a ) is not a function of ID: PCALCZ..7+ Objective: (.) Determine Whether an Equation ) is a function of ID: PCALCZ..+ Objective: (.) Determine Whether an Equation ) g shifts the graph of f verticall down units ID: PCALCZ..+ Objective: (.) Graph Functions b Plotting Points ) ID: PCALCZ..7+ Objective: (.) Obtain Information About a Function from 0 ) domain: [0, ) range: [, ) ID: PCALCZ..8+ Objective: (.) Identif the Domain and Range of a ) Undefined ID: PCALCZ..+ Objective: (.) Calculate a Line's Slope 7) Undefined ID: PCALCZ..8+ Objective: (.) Calculate a Line's Slope 8) 0 ID: PCALCZ..+ Objective: (.) Calculate a Line's Slope 9) + =  ( + ) or + =  ( + 7) ID: PCALCZ..+ Objective: (.) Write the PointSlope Form of the 70) + 7 = (  ) or =  7 ( + ) 8 ID: PCALCZ..+ Objective: (.) Write the PointSlope Form of the 7) m = ; (0, 7) ID: PCALCZ..+ Objective: (.) Recognize and Use the General Form of a 7) = ID: PCALCZ..+ Objective: (.) Write and Graph the SlopeIntercept Form 7) function ID: PCALCZ..8+ Objective: (.) Use the Vertical Line Test to Identif 7) = ID: PCALCZ..7+ Objective: (.) Find Slopes and Equations of Parallel and 7) (, 9) (9, ) (, ) ID: PCALCZ Objective: (.7) Combine Functions Using the Algebra of 7) = ID: PCALCZ..+ Objective: (.) Find Slopes and Equations of Parallel and 77) = ID: PCALCZ..8+ Objective: (.) Find Slopes and Equations of Parallel and
11 Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL 78) ID: PCALCZ..+ Objective: (.) Use Vertical Stretching and Shrinking to 79) ID: PCALCZ..7+ Objective: (.) Graph Functions Involving a Sequence of 80) ID: PCALCZ.7.+ Objective: (.7) Combine Functions Using the Algebra of 8) 0 + ID: PCALCZ.7.+ Objective: (.7) Combine Functions Using the Algebra of 8) (, ) (, ) ID: PCALCZ Objective: (.7) Combine Functions Using the Algebra of 8) Domain: ,  , + +, ID: PCALCZ.7.+ Objective: (.7) Combine Functions Using the Algebra of 8) ID: PCALCZ Objective: (.7) Form Composite Functions 8) (, ) (, ) (, ) ID: PCALCZ.7.+ Objective: (.7) Find the Domain of a Function 8) (, 9] ID: PCALCZ.7.+ Objective: (.7) Find the Domain of a Function 87)  + ID: PCALCZ.7.+ Objective: (.7) Form Composite Functions 88) (, ) (, ) ID: PCALCZ.7.+ Objective: (.7) Determine Domains for Composite 89) [, ) ID: PCALCZ.7.+ Objective: (.7) Determine Domains for Composite 90) f() =, g() = + 0 ID: PCALCZ.7.+ Objective: (.7) Write Functions as Compositions 9) f() = /, g() =  ID: PCALCZ.7.+ Objective: (.7) Write Functions as Compositions 9) g() and h() ID: PCALCZ.8.+ Objective: (.8) Verif Inverse Functions 9) None ID: PCALCZ.8.+ Objective: (.8) Verif Inverse Functions 9) f() = ID: PCALCZ.8.+ Objective: (.8) Find the Inverse of a Function 9)   i ID: PCALCZ..+ Objective: (.) Add and Subtract Comple Numbers 9) ID: PCALCZ..+ Objective: (.) Multipl Comple Numbers 97)  + i ID: PCALCZ..0+ Objective: (.) Multipl Comple Numbers 98) i ID: PCALCZ..+ Objective: (.) Divide Comple Numbers 99) 9i ID: PCALCZ..+ Objective: (.) Perform Operations with Square Roots of 00)  + i 7 ID: PCALCZ..9+ Objective: (.) Perform Operations with Square Roots of 0) + i ID: PCALCZ..+ Objective: (.) Perform Operations with Square Roots of
12 Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL 0) ± i 9 ID: PCALCZ..+ Objective: (.) Solve Quadratic Equations with Comple 0) maimum;, 9 ID: PCALCZ..+ Objective: (.) Determine a Quadratic Function's 0) minimum;, 0) ID: PCALCZ..+ Objective: (.) Determine a Quadratic Function's 0) ID: PCALCZ..+ Objective: (.) Graph Parabolas 0) = 0, = , = ID: PCALCZ..+ Objective: (.) Use Factoring to Find Zeros of Polnomial 07)  ID: PCALCZ..+ Objective: (.) Use Long Division to Divide Polnomials 08) ID: PCALCZ..9+ Objective: (.) Use Snthetic Division to Divide 09) ID: PCALCZ..+ Objective: (.) Use Snthetic Division to Divide   ID: PCALCZ..+ Objective: (.) Graph Eponential Functions ) 0.9 ID: PCALCZ..+ Objective: (.) Evaluate Functions with Base e ) $8,9. ID: PCALCZ..+ Objective: (.) Use Compound Interest Formulas ) $0,000 invested at 8.7% compounded continuousl over 7 ears ields the greater return. ID: PCALCZ..7+ Objective: (.) Use Compound Interest Formulas ) ID: PCALCZ..+ Objective: (.) Graph Eponential Functions ) log = ID: PCALCZ..+ Objective: (.) Change From Eponential to Logarithmic ) = ID: PCALCZ..+ Objective: (.) Change from Logarithmic to Eponential
13 Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL 7) ID: PCALCZ..+ Objective: (.) Evaluate Logarithms 8)  ID: PCALCZ..8+ Objective: (.) Evaluate Logarithms 9) log ( + )  log ID: PCALCZ..+ Objective: (.) Epand Logarithmic Epressions 0)  log (  ) ID: PCALCZ..9+ Objective: (.) Epand Logarithmic Epressions ) log b z8 ID: PCALCZ..+ Objective: (.) Condense Logarithmic Epressions m ) log b n ID: PCALCZ..+ Objective: (.) Condense Logarithmic Epressions ) log  ID: PCALCZ..+ Objective: (.) Use the Quotient Rule
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