4.3 Graph the function f by starting with the graph of y =

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1 Math 0 Eam 2 Review.3 Graph the function f b starting with the graph of = 2 and using transformations (shifting, compressing, stretching, and/or reflection). 1) f() = -2-6 Graph the function using its verte, ais of smmetr, and intercepts. ) f() = ) f() = Determine the quadratic function whose graph is given. ) (0, 1) (1, -1) - - Find the verte and ais of smmetr of the graph of the function. 3) f() = Determine, without graphing, whether the given quadratic function has a maimum value or a minimum value and then find that value. 6) f() = Solve the problem. 7) The owner of a video store has determined that the cost C, in dollars, of operating the store is approimatel given b C() = , where is the number of videos rented dail. Find the lowest cost to the nearest dollar. ) The price p (in dollars) and the quantit sold of a certain product obe the demand equation p = , 0 2. What price should the compan charge to maimize revenue? 1

2 9) You have 20 feet of fencing to enclose a rectangular region. What is the maimum area? ) A projectile is fired from a cliff 200 feet above the water at an inclination of to the horizontal, with a muzzle velocit of 290 feet per second. The height h of the projectile above the water is given b h() = (290) , where is the horizontal distance of the projectile from the base of the cliff. Find the maimum height of the projectile. 1) Solve the problem. 1) If f() = 62 - and g() = 2 + 3, solve f() g()..1 State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 16) f() = ) f() = 3-3. Use the figure to solve the inequalit. 11) g() ) f() = 19) f() = (-, 0) (, 0) Use transformations of the graph of = or = to graph the function. 20) f() = 1 2 ( - ) ) - - For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 21) f() = 2( - 6)( + )2 f() > g() Solve the inequalit. 13) > 0 22) f() = 3(2 + )( + 3)2 2

3 Form a polnomial whose zeros and degree are given. 23) Zeros: -, multiplicit 2; -1, multiplicit 1; degree 3 Find the - and -intercepts of f. 2) f() = ( + 1)( - )( - 1)2 Solve the problem. 29) Which of the following polnomial functions might have the graph shown in the illustration below? Determine the maimum number of turning points of f. 2) f() = -2( + )3(2-1) 26) f() = 9-3 Use the -intercepts to find the intervals on which the graph of f is above and below the -ais. 27) f() = + 1 (- ) 3 3 Analze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of. (b) Find the - and -intercepts of the graph. (c) Determine whether the graph crosses or touches the -ais at each -intercept. (d) Graph f using a graphing utilit. (e) Use the graph to determine the local maima and local minima, if an eist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f b hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. 2) f() = -2( - 1)( + 3) A) f() = 2( - 2)( - 1) B) f() = ( - 2)2( - 1) C)f() = ( - 2)( - 1)2 D) f() = 2( - 2)2( - 1)2.2 Find the domain of the rational function ) R() = Use the graph to determine the domain and range of the function. 31) Find the vertical asmptotes of the rational function ) g() =

4 ) h() = Graph the function. 3 0) f() = (- 2)( + 2) Give the equation of the horizontal asmptote, if an, of the function. 3) h() = ) f() = Give the equation of the oblique asmptote, if an, of the function ) f() = Graph the function using transformations ) f() = - 2 1) f() = ) f() = Find the indicated intercept(s) of the graph of the function. 3) -intercept of f() = ) -intercepts of f() =

5 3) f() = 2 + ( - 2)2 ) f() = Find the intercepts of the function f(). ) f() = Solve the equation in the real number sstem. 6) = Use the Intermediate Value Theorem to determine whether the polnomial function has a zero in the given interval. 7) f() = ; [-1, 0]. Solve the inequalit. ) ( - 1)( - ) > 0 Solve the inequalit. ) 2-6 > 0.6 Information is given about a polnomial f() whose coefficients are real numbers. Find the remaining zeros of f. ) Degree 3; zeros:, 2 - i 9) Degree ; zeros: i, 1 + i 6) > 0 7) 3 ) - + < 0 9) ( + )( - ) Form a polnomial f() with real coefficients having the given degree and zeros. 60) Degree: 3; zeros: - and 3-2i 61) Degree: ; zeros: -1, 2, and 1-2i. Use the given zero to find the remaining zeros of the function. 62) f() = ; zero: - 0) 1) 2 - < - > ) f() = ; zero: 2 + 3i Find all zeros of the function and write the polnomial as a product of linear factors. 6) f() = List the potential rational zeros of the polnomial function. Do not find the zeros. 2) f() = Use the Rational Zeros Theorem to find all the real zeros of the polnomial function. Use the zeros to factor f over the real numbers. 3) f() =

6 Answer Ke Testname: 0 TEST 2 REVIEW 1) ) ) - 3 2,- 37 ; = 3 2 ) verte (-1, -) intercepts (1, 0), (- 3, 0), (0, -3) ) f() = ) minimum; ) $672 ) $1 9) 270 square feet ) 7.03 ft 6

7 Answer Ke Testname: 0 TEST 2 REVIEW 11) { - or }; (-, -] or [, ) ) { < -1 or > 2}; (-, -1) or (2, ) 13) (-, 1) or (6, ) 1) [-9, 0] 1) - 1 3, ) Yes; degree 3 17) Yes; degree 1) Yes; degree 0 19) No; is raised to a negative power 20) ) 6, multiplicit 1, crosses -ais; -, multiplicit 2, touches -ais 22) -3, multiplicit 2, touches -ais 23) ) -intercepts: -1, 1, ; -intercept: - 2) 6 26) 2 27) above the -ais: (, ) below the -ais: -, - 1 3, - 1 3, 7

8 Answer Ke Testname: 0 TEST 2 REVIEW 2) (a) For large values of, the graph of f() will resemble the graph of = -. (b) -intercept: (0, 0), -intercepts: (-3, 0), (0, 0), and (1, 0) (c) The graph of f crosses the -ais at (1, 0) and (-3, 0) and touches the -ais at (0, 0). (e) Local maima at (-2.19,.39) and (0.69, 0.); Local minimum at (0, 0) (f) (-2.19,.39) (-3, 0) (0, 0) (0.69, 0.) (1, 0) (2., -.06) - (g) Domain of f: all real numbers; range of f: (-,.39] (h) f is increasing on (-, -2.19) and (0, 0.69); f is decreasing on (-2.19, 0) and (0.69, ) 29) C 30) -9, 7 31) domain: { -1, 1} range: { 0 or > 1} 32) none 33) = 0, = -16 3) = 2 3) = 0 36) = ) - - 3) (0, 3) 39) (0, 0), (-6, 0)

9 Answer Ke Testname: 0 TEST 2 REVIEW 0) ) )

10 Answer Ke Testname: 0 TEST 2 REVIEW 3) ) (-, 1) or (, ) ) (-, -) or (, ) 6) (-, 0) or (3, ) 7) [, ) ) (-, ) 9) [-, 1) or [, ) 0) (0, 3) or (, ) 1) (-21, -1) or (, ) 2) ± 1, ± 1 2, ± 3, ± 3, ± 1, ± 2, ± 3, ± 6 2 3) -3, -2, 2; f() = ( + 3)( + 2)( - 2) ) 1, 3 ; f() = ( - 1)( - 3)( 2 + ) ) -intercepts: -3, -1, 2; -intercept: -6 6) {-1, 2} 7) f(-1) = -16 and f(0) = 6; es ) 2 + i 9) -i, 1 - i 60) f() = ) f() = ) 3 + 2i, 3-2i 63) 2-3i, 1 6) f() = ( + 1)( + + i)( + - i)