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. - 80-0 - ) Add or subtract terms whenever possible. - - 7 80 ) 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. 7 + 0 ) 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. 8 89 + 8 ) Add or subtract terms whenever possible. 89-87 7) 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. (9 + 98 + 7 + ) - (9 + 8 + 7 + 7) 0) Find the product. ( + )( + 7 + )
) 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. + 8 - - 7) Factor the trinomial, or state that the trinomial is prime. - + ) Multipl or divide as indicated. - + - - ) Multipl or divide as indicated. - 7-7 7) Multipl or divide as indicated. - 7 + 7 + - 7 - - - 7 8) Factor completel, or state that the polnomial is prime. - 9 + - 8) Add or subtract as indicated. + - - 9) Factor completel, or state that the polnomial is prime. + 9) Add or subtract as indicated. + + - - - 0) Factor using the formula for the sum or difference of two cubes. 7 + 0) Add or subtract as indicated. - 8 + 8 - ) 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. + - 9 + 0 ) Simplif the comple rational epression. - +
) Simplif the comple rational epression. 9 - - 9 ) 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. - - < -8-0 - 9) Solve the quadratic equation using the quadratic formula. + 7 + = 0 - -0 0) 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)}
) 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, -) - - - - - - - - - - 70) 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. - - - - - - - - - - - -
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() = - + 8 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() = - -. - 8) 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 = - 8 + 9; 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() = +
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. - + -7 0) 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. - + -0 0) Find the zeros of the polnomial function. f() = + - 0 07) Divide using long division. (- + 8 - ) (- + ) 08) Divide using snthetic division. ( - - 7 + - + 8) ( + ) 09) Divide using snthetic division. + - -
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
Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL ) ID: PCALCZ 0..-+ Objective: (0.) Evaluate Algebraic Epressions ) - 8 ID: PCALCZ 0..-9+ Objective: (0.) Evaluate Algebraic Epressions ) {,, 9, 0, } ID: PCALCZ 0..-+ Objective: (0.) Find the Union of Two Sets ) 8 ID: PCALCZ 0..-+ Objective: (0.) Recognize Subsets of the Real Numbers ) 0 ID: PCALCZ 0..7-8+ Objective: (0.) Evaluate Absolute Value ) Commutative propert of multiplication ID: PCALCZ 0..9-+ Objective: (0.) Identif Properties of the Real Numbers 7) ID: PCALCZ 0..-+ Objective: (0.) Use Properties of Eponents 8) ID: PCALCZ 0..-8+ Objective: (0.) Use Properties of Eponents 9) 9z 9 0) ID: PCALCZ 0..-+ Objective: (0.) Simplif Eponential Epressions 79 ID: PCALCZ 0..-+ Objective: (0.) Simplif Eponential Epressions ) - ID: PCALCZ 0..-+ Objective: (0.) Add and Subtract Square Roots ) - ID: PCALCZ 0..-7+ Objective: (0.) Add and Subtract Square Roots ) 7 + 7 7 ID: PCALCZ 0..-+ Objective: (0.) Rationalize Denominators ) 0-7 ID: PCALCZ 0..-9+ Objective: (0.) Rationalize Denominators ) 8 7 ID: PCALCZ 0..7-7+ Objective: (0.) Evaluate and Perform Operations with ) - 7 ID: PCALCZ 0..7-8+ Objective: (0.) Evaluate and Perform Operations with 7) ID: PCALCZ 0..8-9+ Objective: (0.) Understand and Use Rational Eponents 8) /7z/7 ID: PCALCZ 0..8-0+ Objective: (0.) Understand and Use Rational Eponents 9) 9 + 8-7 - ID: PCALCZ 0..-+ Objective: (0.) Add and Subtract Polnomials 0) + 7 + 8 + 8 ID: PCALCZ 0..-+ Objective: (0.) Multipl Polnomials ) 9 - + - ID: PCALCZ 0..-+ Objective: (0.) Multipl Polnomials ) - ID: PCALCZ 0..-+ Objective: (0.) Use Special Products in Polnomial ) 8 + 8 + 9 + ID: PCALCZ 0..-+ Objective: (0.) Use Special Products in Polnomial ) ( + )( - ) ID: PCALCZ 0..-+ Objective: (0.) Factor the Difference of Squares ) ( - )( - ) ID: PCALCZ 0..-+ Objective: (0.) Factor Out the Greatest Common Factor of ) ( - )( + 8) ID: PCALCZ 0..-+ Objective: (0.) Factor b Grouping 7) ( - )( - ) ID: PCALCZ 0..-+ Objective: (0.) Factor Trinomials 8) ( - )( + )( - ) ID: PCALCZ 0..7-7+ Objective: (0.) Use a General Strateg for Factoring 9) ( + )( - + ) ID: PCALCZ 0..7-+ Objective: (0.) Use a General Strateg for Factoring 8
Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL 0) ( + )(9 - + ) ID: PCALCZ 0..-+ Objective: (0.) Factor the Sum and Difference of Two ) ( - )( + + ) ID: PCALCZ 0..-+ Objective: (0.) Factor the Sum and Difference of Two ), ID: PCALCZ 0..-7+ Objective: (0.) Specif Numbers That Must Be Ecluded ) +, -, - ID: PCALCZ 0..-+ Objective: (0.) Simplif Rational Epressions ) - 7 ID: PCALCZ 0..-+ Objective: (0.) Divide Rational Epressions ) ID: PCALCZ 0..-+ Objective: (0.) Divide Rational Epressions ) 8 7 ID: PCALCZ 0..-+ Objective: (0.) Multipl Rational Epressions 7) - 8 + 9 8) ID: PCALCZ 0..-+ Objective: (0.) Multipl Rational Epressions - - ( + )( - ) ID: PCALCZ 0..-+ Objective: (0.) Add and Subtract Rational Epressions 9) - - 0) - ) ID: PCALCZ 0..-7+ Objective: (0.) Add and Subtract Rational Epressions - 8 ID: PCALCZ 0..-+ Objective: (0.) Add and Subtract Rational Epressions - + ID: PCALCZ 0..-+ Objective: (0.) Simplif Comple Rational Epressions ) 9 ID: PCALCZ 0..-+ Objective: (0.) Simplif Comple Rational Epressions ) {9, -} ID: PCALCZ 0.7.-+ Objective: (0.7) Solve Equations Involving Absolute Value ) {-,, } ID: PCALCZ 0.7.-8+ Objective: (0.7) Solve Equations Involving Absolute Value ) c = ab a + b ID: PCALCZ 0.7.-0+ Objective: (0.7) Solve a Formula for a Variable A - Bh ) b = h ID: PCALCZ 0.7.-+ Objective: (0.7) Solve a Formula for a Variable 7) {} ID: PCALCZ 0.7.-+ Objective: (0.7) Solve Rational Equations with Variables in 8) 9) - 0 7 ID: PCALCZ 0.9.-+ Objective: (0.9) Solve Absolute Value Inequalities -7-9 -7 + 9, ID: PCALCZ 0.7.9-+ Objective: (0.7) Solve Quadratic Equations Using the 0) (, ] - - 0 7 8 9 0 ID: PCALCZ 0.9.-+ Objective: (0.9) Solve Compound Inequalities ) { 7} -0-9-8-7------ 0 7 8 9 0 ID: PCALCZ 0.9.-+ Objective: (0.9) Use Interval Notation ) { - } -0-9-8-7------ 0 7 8 9 0 ID: PCALCZ 0.9.-+ Objective: (0.9) Use Interval Notation ) [-, 0) ID: PCALCZ 0.9.-+ Objective: (0.9) Find Intersections and Unions of Intervals 9
Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL ) (, ) ID: PCALCZ 0.9.-+ Objective: (0.9) Find Intersections and Unions of Intervals ) - -, - + ID: PCALCZ 0.7.9-+ 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 = - 7 8 ( - ) 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) = 7 8 - ID: PCALCZ..-+ Objective: (.) Write and Graph the Slope-Intercept Form 7) function ID: PCALCZ..-8+ Objective: (.) Use the Vertical Line Test to Identif 7) = - + 0 ID: PCALCZ..-7+ Objective: (.) Find Slopes and Equations of Parallel and 7) (-, -9) (-9, ) (, ) ID: PCALCZ.7.-9+ Objective: (.7) Combine Functions Using the Algebra of 7) = - + 7 ID: PCALCZ..-+ Objective: (.) Find Slopes and Equations of Parallel and 77) = - 8 + ID: PCALCZ..-8+ Objective: (.) Find Slopes and Equations of Parallel and
Answer Ke Testname: PRACTICE FINAL EXAM INTRO TO CALCULUS FALL 78) 0 8-0 -8 - - - - 8 0 - - -8-0 ID: PCALCZ..-+ Objective: (.) Use Vertical Stretching and Shrinking to 79) 0 8-0 -8 - - - - 8 0 - - -8-0 ID: PCALCZ..7-+ Objective: (.) Graph Functions Involving a Sequence of 80) 8 + - 0 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.7.-7+ Objective: (.7) Combine Functions Using the Algebra of 8) Domain: -, - -, + +, ID: PCALCZ.7.-+ Objective: (.7) Combine Functions Using the Algebra of 8) + + 9 ID: PCALCZ.7.-7+ 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-() = 8 + 8 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) - 0 7 + 7 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
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) 0-0 - 0 - -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) - + - + 9 + 0 + ID: PCALCZ..-9+ Objective: (.) Use Snthetic Division to Divide 09) + + + 0 + 0 + - 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
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