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. 9-7 ) 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. 9-9 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 set-builder 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 set-builder 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 point-slope form. Passing through (-, -) and (-7, -) ) Use the given conditions to write an equation for the line in point-slope 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 slope-intercept 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; slope-intercept 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 slope-intercept 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 = ; slope-intercept 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() = 9-87) 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 one-to-one function. f() = 8-9) 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. e-0. ) 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 ) 0-7 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 Point-Slope Form of the 70) + 7 = ( - ) or = - 7 ( + ) 8 ID: PCALCZ..-+ Objective: (.) Write the Point-Slope 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 Slope-Intercept 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

MATH 0312 FINAL EXAM REVIEW ITEMS

MATH 0312 FINAL EXAM REVIEW ITEMS MATH 012 FINAL EXAM REVIEW ITEMS Name The items on this review are representative of the items that ou might see on our course final eam. No formul sheets are allowed and calculators are not allowed on