SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Transcription

1 math 11 practice test#. These are eamples of problems that in addition to the notes, quizzes and homework will be on the test. In addition up to 0% of the test will be made up of prior material not on this practice test. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Determine whether the function is a polnomial function. 1) f() = - 1) ) f() = ) 3) f() = ) Find the degree of the polnomial function. ) f() = π ) Find the -intercepts of the polnomial function. State whether the graph crosses the -ais, or touches the -ais and turns around, at each intercept. ) = 0 ) ) f() = -( + 9)( - 1) ) Find the -intercept of the polnomial function. 7) f() = ( + 1)( - )( - 1) 7) Use the Leading Coefficient Test to determine the end behavior of the polnomial function. 8) f() = ) 9) f() = ) Find the zeros of the polnomial function. ) f() = ) Find the zeros for the polnomial function and give the multiplicit for each zero. State whether the graph crosses the -ais or touches the -ais and turns around, at each zero. 11) f() = - + ( + )3 11) 1) f() = 1 ( - )( - ) 1) 1

2 Complete the following: (a) Use the Leading Coefficient Test to determine the graph's end behavior. (b) Find the -intercepts. State whether the graph crosses the -ais or touches the -ais and turns around at each intercept. (c) Find the -intercept. (d) Graph the function. 13) f() = ( + ) 13) Divide using long division. 1) + 1-1) 1) ( ) (3 + 1) 1) Divide using snthetic division. 1) ) 17) ( + 19) ( - ) 17) Use snthetic division and the Remainder Theorem to find the indicated function value. 18) f() = ; f(-) 18) 19) f() = ; f(3) 19) Write the equation of a polnomial function with the given characteristics. Use a leading coefficient of 1 or -1 and make the degree of the function as small as possible. 0) Crosses the -ais at -, 0, and ; lies below the -ais between - and 0; lies above the 0) -ais between 0 and.

3 Graph the polnomial function. 1) f() = - 1) ) f() = ) 3) f() = -3( - 1)( + 1) 3) Use the Rational Zero Theorem to list all possible rational zeros for the given function. ) f() = ) ) f() = ) 3

4 Solve the polnomial equation. In order to obtain the first root, use snthetic division to test the possible rational roots. ) = 0 ) 7) = 0 7) 8) = 0 8) Find the domain of the rational function ) h() = + 3 9) 30) h() = ) ) g() = ) Find the vertical asmptotes, if an, of the graph of the rational function. 3) h() = ( - ) 3) 33) g() = ) Find the horizontal asmptote, if an, of the graph of the rational function. 3 3) h() = + 1 3) 3) g() = + 1 3) 8 3) f() = + 1 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph the rational function.

5 37) f() = ) A) B) C) D) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the slant asmptote, if an, of the graph of the rational function. 38) f() = ) 39) f() = )

6 Solve the polnomial inequalit and graph the solution set on a number line. Epress the solution set in interval notation. 0) > 0 0) Approimate the number using a calculator. Round our answer to three decimal places. 1) 7 1) Graph the function b making a table of coordinates. ) f() = 3 ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph of an eponential function is given. Select the function for the graph from the functions listed. 3) 3) A) f() = B) f() = + 1 C)f() = - 1 D) f() = - 1

7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the function. ) Use the graph of f() = to obtain the graph of g() = -. ) ) Use the graph of f() = 3 to obtain the graph of g() = ) Approimate the number using a calculator. Round our answer to three decimal places. ) e-.7 ) Use the compound interest formulas A = P1 + r n nt and A = Pe rt to solve. 7) Find the accumulated value of an investment of $000 at 8% compounded semiannuall for 8 ears. 7) 8) Find the accumulated value of an investment of $000 at 7% compounded continuousl for ears. 8) 9) Find the accumulated value of an investment of $1,000 at 1% compounded annuall for 7 ears. 9) Write the equation in its equivalent eponential form. 0) log = 0) 7

8 Write the equation in its equivalent logarithmic form. 1) 3 33 = 7 1) Evaluate the epression without using a calculator. ) log ) 3) log 3 3 3) ) log 1 ) ) log 1 ) Graph the function. ) Use the graph of log 3 to obtain the graph of f() = log 3 ( - 1). ) Graph the functions in the same rectangular coordinate sstem. 7) f() = 1 and g() = log 1/ 7)

9 Graph the function. 8) Use the graph of f() = ln to obtain the graph of g() = - - ln. 8) - - Find the domain of the logarithmic function. 9) f() = ln (7 - ) 9) 0) f() = log ) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 1) log 1) 7 ) log - ) 3) ln 8 e 3) Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic epressions. ) 1 log + log ) ) (log a q - log a r) + log a p ) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places ) log 9 17 ) 7) log ) Solve the equation b epressing each side as a power of the same base and then equating eponents. 8) (7-3) = 1 8) 9

10 9) 3(3 + ) = 1 7 9) Solve the eponential equation. Epress the solution set in terms of natural logarithms. 70) 8 = 3. 70) 71) + = + 71) Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 7) e - - = 118 7) 73) = 73) Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. 7) + 8 ln = 8 7) 7) log 9 ( - 8) = 1 7) 7) log ( + ) - log ( - 3) = 1 7) 77) log ( - ) = log (3 + 7) 77) 78) log ( + 3) = + log ( - ) 78) 79) ln ( - ) + ln ( + 1) = ln ( - 1) 79) Solve. 80) The population of a certain countr is growing at a rate of 1.8% per ear. How long will it take for this countr's population to double? Use the formula t = ln, which gives the k time, t, for a population with growth rate k, to double. (Round to the nearest whole ear.) 81) A fossilized leaf contains 1% of its normal amount of carbon 1. How old is the fossil (to the nearest ear)? Use 00 ears as the half-life of carbon 1. 80) 81) Solve the eponential equation. Use a calculator to obtain a decimal approimation, correct to two decimal places, for the solution. 8) = )

11 Answer Ke Testname: PRACTICE TEST 11 # 1) Yes ) No 3) No ) ) 0, crosses the -ais;, crosses the -ais; -, crosses the -ais; 3, crosses the -ais; - 3, crosses the -ais ) 0, touches the -ais and turns around; -9, crosses the -ais; -1, crosses the -ais; 1, crosses the -ais 7) - 8) falls to the left and falls to the right 9) rises to the left and falls to the right ) = 0, = - 7, = 11) -, multiplicit 1, crosses -ais; -, multiplicit 3, crosses -ais 1) 0, multiplicit, touches -ais and turns around;, multiplicit 1, crosses -ais;, multiplicit 1, crosses -ais; -, multiplicit 1, crosses -ais 13) (a) falls to the left and rises to the right (b) -intercepts: (0, 0), touches -ais and turns; (-, 0), crosses -ais (c) -intercept: (0, 0) (d) (-, 0) ) ) 3-3 1) (0, 0) 3-17) ) ) 708 0) f() = ) ) 3) ) ± 1, ± ) ± 1 7, ± 3 7, ± 1, ± 3 ) - 1,, 7) {, +, - }

12 Answer Ke Testname: PRACTICE TEST 11 # 8) {-1,, 1 + i, 1 - i} 9) { 0, -3} 30) { -, } 31) all real numbers 3) = 0 and = 33) =, = - 3) no horizontal asmptote 3) = 3) = 0 37) C 38) no slant asmptote 39) = + 9 0) (-, -) (-3, ) 1) 39.1 ) ) ) ) $11, ) $7.7 9) $33,. 0) = 1) log 33 7 = 1 3 ) 3) ) - ) 0 ) 3) D )

13 Answer Ke Testname: PRACTICE TEST 11 # 7) ) {} 77) 7 78) 3 79) 80) 39 ears 81) 1,99 8) ) - - 9) (-, 7) 0) (-, -7) (8, ) 1) log - 7log ) log ( - ) - log 3) 1 8 ln ) log ) log a qp r ) ) ) {3} 9) {-3} ln 3. 70) ln 8 71) 7) ) ) e 1/ 7) {9, -1} ln - ln ln - ln 13