135 Final Review. Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and/or the origin.

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1 13 Final Review Find the distance d(p1, P2) between the points P1 and P2. 1) P1 = (, -6); P2 = (7, -2) Determine whether the graph is smmetric with respect to the -ais, the -ais, and/or the origin. Identif whether the triangle formed b the three vertices given is isosceles, right, neither of these, or both. 2) (7, 10), (9, 14), (11, 13) right isosceles both neither Find the midpoint of the line segment joining the points P1 and P2. 3) P1 = (1, 9); P2 = (2, 2) (3, 11) ( 11 2, 3 2 ) ( 3 2, 11 ) (-1, 7) 2 List the intercepts of the graph. 6) - - -ais origin -ais -ais, -ais, origin E) none 4) (0, -3), (3, 0), (0, 1) (0, -3), (0, 3), (1, 0) (-3, 0), (0, 3), (1, 0) (-3, 0), (0, 3), (0, 1) List the intercepts for the graph of the equation. ) = 0 (-7, 0), (0, -49), (7, 0) (-7, 0), (0, 49), (7, 0) (7, 0), (0, 49), (0, -49) (0, -7), (49, 0), (0, 7) 7) -ais origin -ais - -ais, -ais, origin E) none Determine whether the graph of the equation is smmetric with respect to the -ais, the -ais, and/or 8) = 0 -ais origin -ais -ais, -ais, origin E) none 1

2 9 9) = ais origin -ais -ais, -ais, origin E) none Solve the problem. 10) If a graph is smmetric with respect to the -ais and it contains the point (, -6), which of the following points is also on the graph? (-, 6) (-6, ) (-, -6) (, -6) Write the standard form of the equation of the circle with radius r and center (h, k). 11) r = ; (h, k) = (-2, -6) Solve the problem. ( + 2)2 + ( + 6)2 = 2 ( - 2)2 + ( - 6)2 = ( + 2)2 + ( + 6)2 = ( - 2)2 + ( - 6)2 = 2 12) Find the equation of a circle in standard form where C(6, -2) and D(-4, 4) are endpoints of a diameter. ( + 1)2 + ( + 1)2 = 34 ( - 1)2 + ( - 1)2 = 136 ( - 1)2 + ( - 1)2 = 34 ( + 1)2 + ( + 1)2 = 136 Find the slope of the line containing the two points. 13) (-8, 8); (1, 8) undefined Find the slope of the line through the points and interpret the slope. 14) (1, -3); (7, 8) 6 ; for ever 11-unit increase in, will 11 increase b 6 units - 11 ; for ever 6-unit increase in, 6 will decrease b 11 units Solve the problem. - 6 ; for ever 11-unit increase in, 11 will decrease b 6 units 11 ; for ever 6-unit increase in, will 6 increase b 11 units 1) Find an equation of the line with slope undefined and containing the point (1, 7). = 7 = 7 = 1 = 1 Find the slope-intercept form of the equation of the line with the given properties. 16) slope = 0; containing the point (-6, 8) Solve the problem. = 8 = 8 = -6 = -6 17) Find the general form of the equation of the line containing the points (8, -3) and (-4, 2) = = = = 4 Find the slope-intercept form of the equation of the line with the given properties. 18) slope = 4; containing the point (-3, -8) = = -4-4 = = ) -intercept = ; -intercept = 3 = = = =

3 Find an equation for the line with the given properties. 20) Parallel to the line = 21; containing the point (3, 2) = = = = 17 21) Perpendicular to the line -7-3 = -11; containing the point (2, 1) Solve the problem. 3-7 = = = = -1 22) A truck rental compan rents a moving truck one da b charging $3 plus $0.11 per mile. Write a linear equation that relates the cost C, in dollars, of renting the truck to the number of miles driven. What is the cost of renting the truck if the truck is driven 140 miles? C = ; $0.40 C = ; $19.60 C = ; $ C = ; $36.4 Determine whether the relation represents a function. If it is a function, state the domain and range. 23) Alice Brad Carl snake cat dog function domain: {Alice, Brad, Carl} range: {snake, cat, dog} function domain: {snake, cat, dog} range: {Alice, Brad, Carl} not a function Find the value for the function. 24) Find f(-1) when f() = Determine whether the relation represents a function. If it is a function, state the domain and range. 2) {(-2, 6), (2, 4), (4, 1), (8, -2)} function domain: {6, 4, 1, -2} range: {-2, 2, 4, 8} function domain: {-2, 2, 4, 8} range: {6, 4, 1, -2} not a function Find the value for the function. 26) Find f(-) when f() = ) Find f( - 1) when f() = Find the domain of the function. 28) f() = { -6} { -6} { > -6} all real numbers 3 29) g() = 2-36 { > 36} { -6, 6} { 0} all real numbers ) h() = { 1} all real numbers { -2, 0, 2} { 0} 3

4 31) f() = 11 - { 11} { 11} { 11} { 11} Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. 32) - - function domain: { -2 2} range: all real numbers intercepts: (-2, 0), (2, 0) smmetr: -ais, -ais function domain: { -2 or 2} range: all real numbers intercepts: (-2, 0), (2, 0) smmetr: -ais, -ais, origin function domain: all real numbers range: { -2 or 2} intercepts: (-2, 0), (2, 0) smmetr: -ais not a function For the given functions f and g, find the requested function and state its domain. 33) f() = 2 - ; g() = - 8 Find f - g. (f - g)() = 3-3; all real numbers (f - g)() = -3-13; { } (f - g)() = 7-13; { 1} (f - g)() = ; all real numbers 34) f() = 16-2; g() = 4 - Find f + g. (f + g)() = ; all real numbers (f + g)() = ; all real numbers (f + g)() = ; { 4, -} (f + g)() = 4 + ; { -4} Find and simplif the difference quotient of f, f( + h) - f(), h 0, for the function. h 3) f() = h 2 + 4( - 1) h 2 The graph of a function f is given. Use the graph to answer the question. 36) Is f(40) positive or negative? positive negative Determine algebraicall whether the function is even, odd, or neither. 37) f() = even odd neither 4

5 38) even odd neither -3 39) f() = 42 + even odd neither The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. 40) (0, 1) The graph of a function f is given. Use the graph to answer the question. 42) Find the numbers, if an, at which f has a local maimum. What are the local maima? -π 2 -π π 2 2 π -2 f has a local maimum at -π; the local maimum is 2 f has a local maimum at = 0; the local maimum is -2 f has a local maimum at = -π and π; the local maimum is 2 f has no local maimum constant decreasing increasing 41) (, ) (-8, ) 10 (2.2, 3.9) (-, 0) (4, 0) -10 (-9., 0) (0, 0) 10 (-2., -3.3) (, -2.) -10 constant decreasing increasing For the function, find the average rate of change of f from 1 to : f() - f(1), ) f() = ( + 8) ( - 1)( + 8) Match the graph to the function listed whose graph most resembles the one given. 44) absolute value function square function reciprocal function cube function

6 4) Graph the function. 49) f() = - if < 1 4 if 1 square function cube root function square root function cube function ) square root function cube function cube root function square function ) absolute value function - square function - square root function reciprocal function 48) - square function - cube function square root function cube root function 6

7 0) f() = < Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 1) f() =

8 2) f() = ( + 4)2 3) f() = ( - 3)

9 4) f() = 1-3 ) f() = (-)

10 6) f() = 2( + 1) ) f() =

11 Solve the problem. 8) A wire of length 3 is bent into the shape of a square. Epress the area A of the square as a function of. A() = A() = A() = A() = Find the verte and ais of smmetr of the graph of the function. 9) f() = (-4, 0); = -4 (4, 32); = 4 (-4, 32); = -4 (4, 0); = 4 60) f() = Solve the problem. (-3, -37); = -3 (-3, 107); = -3 (3, 107); = 3 (3, 3); = 3 61) 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. $462 $631 $716 $88 State whether the function is a polnomial function or not. If it is, give its degree. If it is not, tell wh not. 62) f() = ( - 10) No; it is a product Yes; degree 2 Yes; degree 1 Yes; degree 0 63) f() = ( - 11) Graph the function using its verte, ais of smmetr, and intercepts. 64) f() = verte (-2, 1) intercepts (-1, 0), (- 3, 0), (0, -3) - - verte (2, 1) intercepts (1, 0), (3, 0), (0, -3) - - verte (-2, -1) intercepts (-1, 0), (- 3, 0), (0, 3) - - verte (2, -1) intercepts (1, 0), (3, 0), (0, 3) Yes; degree 0 No; it is a product Yes; degree 2 Yes; degree

12 Use transformations of the graph of = 4 or = to graph the function. 6) f() = ) f() = -2( + 3)

13 Form a polnomial whose zeros and degree are given. 67) Zeros: -3, -1, 2; degree 3 f() = for a = 1 f() = for a = 1 f() = for a = 1 f() = for a = 1 For the polnomial, list each real zero and its multiplicit. Determine whether the graph crosses or touches the -ais at each -intercept. 68) f() = 2( - )( - 4)2 -, multiplicit 1, touches -ais; -4, multiplicit 2, crosses -ais, multiplicit 1, touches -ais; 4, multiplicit 2, crosses -ais -, multiplicit 1, crosses -ais; -4, multiplicit 2, touches -ais, multiplicit 1, crosses -ais; 4, multiplicit 2, touches -ais Give the equation of the specified asmptote(s) ) Vertical asmptote(s): f() = = -7, = 2 = 7, = 7, = -2 3 = 7, = -2 no vertical asmptotes Find the indicated intercept(s) of the graph of the ) -intercepts of f() = (0, 0) and (-7, 0) (-7, 0) (7, 0) (0, 0) and (7, 0) ) -intercepts of f() = (, 0) (0, 0) and (, 0) (-, 0) Solve the inequalit. (0, 0) and (-, 0) 72) (-, 2] [4, ) [2, 4] (-, 2] or [4, ) 73) > 0 74) (-, -6) or (4, ) (-, -6) (4, ) (-6, 4) 1-4 > 12-1 (-11, 1) or (4, ) (-, -11) or (1, 4) (-11, 1) or (1, 4) (-, -11) or (4, ) Use the Factor Theorem to determine whether - c is a factor of f(). 7) f() = ; + 9 Yes No 76) f() = ; - 10 Yes No 13

14 List the potential rational zeros of the polnomial function. Do not find the zeros. 77) f() = ± 1 3, ± 1, ± 1, ± 2, ± 3 2 ± 1 3, ± 2, ± 1, ± 2, ± 3 3 ± 1 2, ± 3 2, ± 1, ± 3 ± 1 3, ± 2 3, ± 1, ± 2 Find all of the real zeros of the polnomial function, then use the real zeros to factor f over the real numbers. 78) f() = , -, 1; f() = ( + 2)(2 + )( - 1) 2 -, -1, 2; f() = (2 + )( + 1)( - 2) 2-2,, 1; f() = ( + 2)(2 - )( + 2) 2 2; f() = ( - 2)( ) Solve the equation in the real number sstem. Find the inverse. Determine whether the inverse represents a function. 82) {(20, 7), (-8, 7), (1, 9)} {(7, 20), (7, -8), (9, 1)}; not a function {(7, 20), (1, -8), (9, 7)}; not a function {(7, 20), (7, -8), (9, 1)}; a function {(20, 7), (7, -8), (9, 1)}; not a function Decide whether or not the functions are inverses of each other. 83) f() = 9 + 6; g() = 9-6 Yes No If the following defines a one-to-one function, find the inverse. 84) f() = ( + 2)3-8. f-1() = f-1() = f-1() = f-1() = ) = 0 { 2,, - } { - 1 2,, - } { 1 2,, - } Solve the equation. 8) 3 - = { -2,, - } Find the indicated composite for the pair of functions. 80) (f g)(): f() = + 8, g() = ) (g f)(): f() = - 9, g() = ) = 64 3, -3 3, Change the logarithmic epression to an equivalent epression involving an eponent. 87) log 2 8 = = = = = 3 14

15 Find the eact value of the logarithmic epression. 88) log Solve the equation. 97) log (2 + ) - log ( - 2) = log ) log ) ln e 91) ln l e 1-1 e 0 Find the domain of the function. 92) f() = log ( - ) > 1 > - > 0 > Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. 93) ln e e Solve the sstem of equations b substitution. 98) + 7 = = 34 = 7, = 12 = 12, = -2 = 3, = 7 = -2, = 3 Solve the sstem of equations b elimination. 99) = = 38 = 10, = -3 = 3, = -10 = -3, = 10 = -10, = 3 Solve the sstem of equations. 100) + + z = z = z = -11 = -4, =, z = -2 = -2, = -4, z = = -2, =, z = -4 inconsistent 94) log log ) log log ) log 4 13 log

16 Answer Ke Testname: 13 STUDY GUIDE FALL 0 1) C 2) A 3) C 4) C ) B 6) E 7) A 8) C 9) B 10) C 11) A 12) C 13) B 14) D 1) C 16) A 17) A 18) C 19) B 20) B 21) A 22) A 23) C 24) B 2) B 26) B 27) A 28) D 29) B 30) C 31) C 32) D 33) D 34) C 3) D 36) B 37) A 38) A 39) B 40) B 41) C 42) C 43) D 44) B 4) C 46) B 47) D 48) D 49) A 0) C 16 1) B 2) B 3) A 4) D ) D 6) A 7) B 8) C 9) B 60) A 61) C 62) B 63) C 64) C 6) C 66) B 67) A 68) D 69) C 70) A 71) D 72) D 73) A 74) A 7) A 76) B 77) D 78) B 79) C 80) A 81) D 82) A 83) B 84) B 8) B 86) A 87) B 88) D 89) B 90) B 91) D 92) D 93) B 94) C 9) D 96) D 97) A 98) B 99) A 100) C