Answers. Chapter 4. Cumulative Review Chapters 1 3, pp Chapter Self-Test, p Getting Started, p a) 49 c) e)

Size: px

Start display at page:

Download "Answers. Chapter 4. Cumulative Review Chapters 1 3, pp Chapter Self-Test, p Getting Started, p a) 49 c) e)"

Nickolas Dalton
5 years ago
Views:

1 . 7" " " 7 "7.. "66 ( ") cm. a, (, ), b... m b.7 m., because t t has b ac 6., so there are two roots. Because parabola opens down and is above t-ais for small positive t, at least one of these roots is positive. 6. k,. or k.. 7. bikes. f (). The famil of parabolas will all have verte (, ); f () ( ). f () 7 about. m. (, ), (.,.)., after s. Height is m.., the will not intersect. The discriminant of f () g() is 7. There are no real solutions for f () g(), meaning that f () and g() do not intersect. will var. For eample, g(). Cumulative Review Chapters, pp. 6 $. ( 7. (. (. (. (. (. (. (. (. ( 6. (. (. (. (. (. ( 7. (. (. ( 6. (. (. (. (. ( 7. (. (. ( 6. (. (. (. (. (. Domain: { [ R}, Range: { [ R }; Parent function: ; Transformations: Vertical stretch b a factor of, horizontal translation right, vertical translation up; Graph: Domain: { [ R $ }, Range: { [ R # }; Parent function:!; Transformations: Vertical stretch b a factor of, reflection in the -ais, horizontal compression b a factor of, horizontal translation left, vertical translation up; Graph: Chapter Self-Test, p.. f () ( ), verte (, ) zero at, ais of smmetr, opens down domain { [ R}; range { [ R # } 6 Domain: { [ R 6}, Range: { R }; Parent function: [ ; Transformations: Horizontal stretch b a factor of, horizontal translation 6 to the right, vertical translation down; Graph: f() = +. Maimum value; complete the square. Minimum value; average the zeros.. Verte form; verte is visible in equation. Standard form; -intercept is visible in equation. Factored form; zeros are visible in equation. Verte form; use -coordinate of verte. e) Verte form.; use verte and direction of opening.. 6 m. f 6 Å 6. " " " " " can be simplified to ". This resulted in like radicals that could be combined. 7. k or. Intersects in places, since 6 has b ac. ; (, ), (., 6). f (). Jill:.6 km/h, h min; Sacha: km/h; 6 h min (including time to stop and talk with frien. or students about $7 Chapter Getting Started, p.. e) 6

2 . 6 e) 7 6. () will result in a positive answer since the eponent is an even number.. 6 e) e) a 7 b c d. m a r. V. cm V 6. cm. first differences are all ; linear function first differences are,,,, ; second differences are all ; quadratic function Lesson., p. 6. Both graphs decrease rapidl at the beginning, then continue to decrease less rapidl before levelling off. º C º C. Number of Squares Number of Grains on the Chessboard on that Square First Differences Number of grains on that square Number of squares on chessboard The are similar in that both first difference tables show a multiplicative pattern. The are different in that in the first case, the values decrease sharpl and then level off while in the second case, the values start level and then increase sharpl. Lesson., pp.. e) a b a () 6 b 7. () e) 6 7. is less than a b. 6 e) 6 () 7. e) 6. 6 e) e) 6. e) 6. e) ,,,,, (.) ; If the numerators of the numbers are all the same (), then the larger the denominator, the smaller the number Erik: (negative eponents do not make numbers negative) Vinn: and he did not add the eponents correctl. Correct solution: 66

3 . e) 6 g) 6 i) 7 7 h) 6 6. e) g) h). ( ) is multiplied b itself three times. is the reciprocal of cubed. ( ) is multiplied b itself four times. is the negative of. 6. e) n 7. n w. r b mn e) a p b mn r 6m m Lesson., pp..! 7 " e) "! " 6!. ( 6) 7776 (7) e) a b 7 a 6 b. () e) e) 6. 6 e) e) m. 7, The values are not equal as...., an odd root,., an even root. Even root of a negative number is not real.. ( ).. e) (!). Change. to a fraction as. This is the same as taking the square root of the four and then taking the fifth power of that result.. false false e) false false true true. ma var. For eample, m, n. n 6. The value of can equal the value of. Also and. 7. this works. The value of i is approimatel Lesson., pp m e) p a k. e) w b. 6 6 Usuall it is faster to substitute numbers into the simplified form.. p q a b 7 e) w 6. 7 e) a n n 6 m 6 m b n 6. e) 6m c 7. 6 b p. a n m 6 6. m n 7 a ". M 6 ma var. For eample,, ma var. For eample,, ma var. For eample,,. h r SA V.67 cm hr. These simplif to,,, respectivel. Switch 7 second and third for proper order.. Algebraic and numerical epressions are similar in the following wa: when simplifing algebraic or numerical epressions, ou have to follow the order of operations. When simplifing algebraic epressions, ou can onl add or subtract like terms while unlike terms ma be multiplied. In this wa algebraic epressions are different than numerical epressions.. r V Å p a V p b m. a 6 b r p 7 67

4 Mid-Chapter Review, p.. e) a b a b cannot be zero or a negative number for. can be zero for, but not negative. 7. e) 6. Eponential Form Radical Form Evaluation of Epression " 7 Lesson.6, pp.. The function moves up units. It is a vertical translation. The function moves to the left units. It is a horizontal translation. The function values are decreased b a factor of. It is a vertical compression. The -values are increased b a factor of. It is a horizontal stretch.. The base function is. Horizontal translation left unit, vertical stretch of factor, and reflection in -ais. The base function is a. Vertical stretch factor, horizontal b compression of factor, and vertical translation of units up. The base function is a. Vertical stretch factor 7, and b. translation of unit down and units to the right. The base is. Horizontal compression b a factor of and a translation units to the right. Function -intercept Asmptote Domain Range e) 6. " 6 " (7) " (7). " 6 7 " [ R., [ R 7 [ R., [ R ( ) [ R., [ R [ R., [ R and () (" ) () 6 (" ) () 6 The second epression has an even root so the negative sign is eliminated.. e) 6 a n.. e).7 n a 6 b m c b. a b a. a p m 66m nm ( ) [ R,, [ R a b [ R., [ R 7(. ) [ R., [ R 6 6. [ R., [ R. horizontal compression of factor, reflect in -ais vertical stretch of factor, reflect in -ais, translate units right vertical stretch of factor, horizontal compression of factor, reflect in the -ais, translate units left and 6 units down Lesson., p.. quadratic eponential eponential linear. eponential; the values decrease at a fast rate eponential; the values increase at a fast rate linear; straight line quadratic; graph is a parabolic shape 6

5 . Function Transformations -intercept Asmptote Domain Range.f () f (. ) f ( 6) f(. ) vertical compression. [ R., [ R b a factor of reflection in the -ais translation of units up reflection in the -ais [ R,, [ R horizontal stretch of translation down and left reflection in the -ais [ R,, [ R 6 vertical stretch of horizontal compression b factor of translation units right reflection in the -ais [ R., [ R horizontal stretch of horizontal translation of units right 6. Both functions have the -intercept of and the asmptote is. Their domains are all real numbers and their ranges are.. The second function will increase at a faster rate. 7. Temperature ( C) Water Temperature vs. Time = (.) / + Time (min) The -intercept represents the initial temperature of C. The asmptote is the room temperature and the lower limit on the temperature of the water.. If the doubling time were changed to, the eponent would t t change from to. The graph would not rise as fast. domain is t $, t [ R; range is N. N, N [ R. (iii) (ii) (iv) (i). 6. Translate down units, translate right unit, and verticall compress b factor... = +. Reflect in the -ais and translate units up. Lesson.7, pp Eponential Growth Initial Growth Function or Deca? Value or Deca Rate V (.) t P (.) n A.() Q 6a b w growth % deca % growth. % deca 6 7.%. persons; it is the value for a in the general eponential function. %; it is the base of the eponent minus. 7. $; it is the value for a in the general eponential function. %; it is the base of the eponent minus. $7. th month after purchase. 6% $ V (.6) n, $ The doubling period is hours. represents the fact that the population is doubling in number (% growth rate). is the initial population. bacteria e) 6 bacteria The population is at a.m. the net da. 7. ( and ( have bases between and. = ( ).+ 6

6 C. 6 During the th ear the population will double. 6 ears ago { n [ R}; { P [ R P $ }. C after min. C (.) w. refers to the percent of the colour at the beginning. refers to the fact that % of the colour is lost during ever wash. w refers to the number of washes. P (.) t refers to the initial population.. refers to the fact that the population grows.% ever ear. t refers to the number of ears after. P P () t refers to the fact that the population doubles in one da. t refers to the number of das.. % 6 P ( t ) e).6 h { t [ R t $ }; { P [ R p $ }. V (.6 t ) $.6 $.. I (. d ) about.%. P (. a ) 6 applications. approimatel.7% 6. P (.7 t ) refers to the initial count of east cells..7 refers to the fact that the cells grow b 7% ever h. t refers to the fact that the cells grow ever h. 7. It could be a model of eponential growth. ma var. For eample,. ma model the situation. There are too few pieces of data to make a model, and the eponential growth cannot continue indefinitel.. eponential deca about.% Chapter Review, pp , if ; If, then... will be less than one and will be greater than one.., if,, and, then will be greater than one and will be less than one.. (7) e) 7 () 6 () 7. 7 p " " m. e) 6. a e) e c 6 d b f. m n e). b a. quadratic eponential e) eponential linear eponential eponential. eponential quadratic eponential. ; horizontal stretch b a factor of and vertical translation of down = ( ) ; vertical compression b a factor of, reflection in the -ais, and translation of unit up ; reflection in the -ais, vertical stretch b a factor of, horizontal compression b a factor of, and translation of left ; reflection in the -ais, = () + vertical compression a factor of, horizontal compression b a factor of, translation of units right and of units up. -intercept asmptote: equation:.. Growth/ Function Deca -int = () + = () + Growth/ Deca Rate V(t) (.) t growth % 6. ("a a b; ("a " a b "ab; so "a b "a "b, for a, b 7. 6 e) 6 w m 6 P(n) (.) n deca % A() () growth % Q(n) 6 a n b deca 6 7.%

7 . The base of the eponent is less than. C Temperature vs. Time Temperature ( C) C e) The in the eponent would be a lesser number. There would be a horizontal compression of the graph; that is, the values would decrease more quickl.. $ $ 7 e) $.% $ $ 6. P (.)n refers to the fact that the pond is covered b lilies.. refers to the % increase in coverage each week. n refers to the number of weeks. A A a b f (t) A refers to the initial amount of U. refers to the half-life of the isotope. t refers to the number of ears. I (.6) n.6 refers to the % decrease in intensit per gel. n refers to the number of gels. 7. P (.) n during 7 7 about 7.% Chapter Self-Test, p. 7. There is a variable in the eponent part of the equation, so it s an eponential equation. If the second differences are, the relation is linear. If the second differences are equal but non-zero, the relation is quadratic. If the second differences show a multiplicative pattern, the relation is eponential. reflection in the -ais, vertical compression of, horizontal compression b a factor of, and translations of left and up = ( + ) + f (t) = ( t ) + t Time (min) t. 6.. a b. I (.6) n.6% As the number of gels increases the intensit decreases eponentiall.. P (.) n, where P is population in millions and n is the number of ears since ears after or in 6. ( 7. n ; n must be odd because ou cannot take even roots of negative numbers. Chapter Getting Started, p. 7. c m f "7 m. sin A, cos A, tan sin D, cos D "7 tan, m 7.. m. ma var. For eample, This question cannot be solved with the sine law. Are ou given an other sides? Are ou given an other angles? Use angle sums to find the unknown angle. A D "7 7 Are ou given a side and opposite angle? Are ou given the side opposite our unknown angle? Use the sine law to solve for the unknown angle. Lesson., pp.. sin A, cos A, tan A, csc A, sec A, cot A. csc u 7, sec u 7, cot u. csc u sec u cot u cot u Use the sine law to find the angle opposite this given side 6

Functions Project Core Precalculus Extra Credit Project

Name: Period: Date Due: 10/10/1 (for A das) and 10/11/1(for B das) Date Turned In: Functions Project Core Precalculus Etra Credit Project Instructions and Definitions: This project ma be used during the