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1 REVIEW Eam #3 : , , 5.1 Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end behavior to match the function with its graph. 1) f() = ) Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the -ais or touches the -ais and turns around, at each zero. 2) f() = 3( + 2)( + 5) 2 2) Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. 3) f() = ; between -1 and 0 3) Graph the polynomial function. 4) f() = ) 5) f() = ) 1
2 Divide using long division. 6) ( ) ( - 7) 6) Divide using synthetic division. 7) ) 8) ) Use synthetic division and the Remainder Theorem to find the indicated function value. 9) f() = ; f(-3) 9) Use the Rational Zero Theorem to list all possible rational zeros for the given function. 10) f() = ) 11) f() = ) Find a rational zero of the polynomial function and use it to find all the zeros of the function. 12) f() = ) 13) f() = ) Find an nth degree polynomial function with real coefficients satisfying the given conditions. 14) n = 3; 3 and i, - i are zeros; f(2) = 25 14) Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 15) f() = ) Find the domain of the rational function. 16) h() = ) Find the vertical asymptotes, if any, of the graph of the rational function. 17) g() = ) 18) g() = ) Find the horizontal asymptote, if any, of the graph of the rational function. 4 19) f() = ) 2
3 20) g() = ) Graph the rational function. 21) f() = ) Find the slant asymptote, if any, of the graph of the rational function. 22) f() = ) Solve the polynomial inequality and graph the solution set on a number line. Epress the solution set in interval notation. 23) ) Solve the rational inequality and graph the solution set on a real number line. Epress the solution set in interval notation. 24) < 3 24) 3
4 Graph the function by making a table of coordinates. 25) f() = 4 25) 26) f() = ) Write the equation in its equivalent logarithmic form. 27) b 3 = ) Evaluate the epression without using a calculator. 28) log ) 29) log ) Write the equation in its equivalent eponential form. 30) log b 64 = 3 30) Evaluate or simplify the epression without using a calculator. 31) log ) 4
5 Graph the function. 32) Use the graph of log 4 to obtain the graph of f() = log 4 ( + 1). 32) Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. 33) log 5 (25) 33) 34) log 10 34) 35) log ) 36) log b (yz 4 ) 36) 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. 37) 3 log b m - log b n 37) 38) 3 log 2 + log 3 38) Solve the equation by epressing each side as a power of the same base and then equating eponents. 39) 5 = 25 39) Solve the eponential equation. Epress the solution set in terms of natural logarithms. 40) e + 5 = 2 40) Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic epressions. Give the eact answer. 41) log 2 ( + 4) - log 2 ( - 2) = 2 41) 42) log 3 = log 4 + log ( - 1) 42) 5
6 Answer Key Testname: REVIEWEXAM_3 1) falls to the left and falls to the right 2) -2, multiplicity 1, crosses -ais; -5, multiplicity 2, touches -ais and turns around 3) f(-1) = -17 and f(0) = 3; yes 4) 5) 6) - 5 7) 4-9 8) ) ) ± 1, ± 3 11) ± 1, ± 7, ± 3, ± 21 12) {-3, -2, 3} 6
7 Answer Key Testname: REVIEWEXAM_3 13) {-2, , -3-7} 14) f() = ) 3 or 1 positive zeros, 2 or 0 negative zeros 16) { -5, 5} 17) = -3 18) = 5, = -5 19) y = 0 20) y = 4 21) 22) y = 23) [-4, -2] 24) (-, -8) or (- 17 2, ) 25) 7
8 Answer Key Testname: REVIEWEXAM_3 26) 27) logb 2744 = 3 28) 2 29) -2 30) b 3 = 64 31) 3 32) 33) 2 + log 5 34) log ) 6 log 7 36) log b y + 4 log b z 37) log b m3 n 38) log 24 39) {2} 40) {ln 2-5} 41) {4} 42) {4} 8
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