Chapter 9 BLM Answers BLM 9 Prerequisite Skills. a) x 5x4 x x x x x x 5x x 5x 5x 4x 4x 0 g(x) x 5x 4. a) g(5 g) g(f 4g) c) (x 5)(x ) d) (x )(x 5) e) (a )(a ) f) (x 0.)(x 0.) g) 5(xy )(xy ). a),, and h(x) (x )(x )(x ) c),, and 5 4. a) b 0, c 0 x c) x, x d) t 5 e) x, x f) a, a, and a 5. a) P() () 5() () 8 0, therefore, (x ) is a factor. P(x) (x )(x 4)(x ) c) x,, 4 d) 7. a) x 7 x, c) x 6 4 d) x e) x, x 0, x 4 f) x 6, x, 8. a) (x 5) 0 (x 4) 0 c) (x ) 0 d) (x ) 5 0 9. a) x 4, x 5,, The x-intercepts are the solution to P(x) 0. 6. a) x 4x 0; 6 and y (x ) 6 c) x 0. a), x, x. a), z 4, 5 k 5, k, k, x,0,5 x BLM 9 Section 9. Extra Practice. a) B C c) D d) A. The x-intercepts are the solution to the equation. The x-coordinate of the vertex is the that makes (x h) 0 and the y-coordinate is equal to k. Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4
5 y x Non-permissible x Behaviour near nonpermissible approaches, y becomes very large. End behaviour As x becomes very large, y approaches 0. Domain {xx, x R} Range {yy 0, y R} Equation of vertical x Equation of horizontal y 0. a) d) domain: {xx, x R}; range: {yy 8, y R}; intercepts: (0, 8.5), (.5, 0); s: x, y 8 4. a) domain: {xx, x R}; range: {yy 0, y R}; intercept: (0, ); s: x, y 0 s: x, y ; intercepts: (.5, 0), (0, 5) domain: {xx 0, x R}; range: {yy 6, y R}; intercept:,0 ; s: x 0, y 6 c) s: x, y 4; intercepts: (0,.5), (0.75, 0) 4 5. a) y y c) y d) x x x 5 6. a) a, k 4 y x 4 domain: {xx 4, x R}; range: {yy, y R}; intercepts: (0, 0.75), (.5, 0); s: x 4, y Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4
7. 9. a) t d s 5 t 5.4, so 5.4 hours or 5 h and 4 min 65 c) 70. km/h The graph of y is the graph of y x 6 x 9 x translated units left. 8. x y 5 0.9 0.56 0.7 4. 7 undefined 0 6. 4.7 6.44 9.08 x y x 7 Non-permissible x 7 Behaviour near nonpermissible End behaviour approaches 7, y becomes very large. As x becomes very large, y approaches. Domain {xx 7, x R} Range {yy, y R} Equation of vertical Equation of horizontal x 7 y BLM 9 Section 9. Extra Practice. point of discontinuity at (, 0 ) vertical : x 7. You can factor the denominator: y x ( x )( x ). Since the factor (x ) appears in the numerator and denominator, the graph will have a point of discontinuity at (, ). The factor (x ) appears in the denominator only, so there will be an at x.. ( x )( x ) y ( x 5)( x ) Non-permissible (s) x 5 and x Feature exhibited at each non-permissible Behaviour near each non-permissible at x 5; point of discontinuity at (,.5) approaches 5, y becomes very large. approaches, y approaches.5. Domain {xx, 5, x R} Range 4. a) x y 0.9. 0.99.0 0.999.00 0.9999.000 undefined.000.9999.00.999.0.99..9 {yy, approaches, y approaches. 5, y R} Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4
x y.9 4.8 095 4.99 4.47 66 8.999 4.497 5 7.9999 4.499 75 0 undefined.000 4.500 75 0.00 4.50 75 8.0 4.57 68 9. 4.789 47 68 x y.9 09.99 099.999 0 999.9999 09 999 4 undefined 4.000 0 00 4.00 00 4.0 0 4. approaches, y approaches 4.5, and as x approaches 4, y becomes very large, approaching negative infinity or positive infinity. 5. a) vertical : x ; point of discontinuity at (5, 5 ); x-intercept: (0, 0); y-intercept: (0, 0) vertical : x ; point of discontinuity at (, ); 6 4 x-intercept: (4, 0); y-intercept: (0, ) c) no vertical ; point of discontinuity at (, ); x-intercept: (4, 0); y-intercept: (0, 4) d) no vertical ; point of discontinuity at (, 7); x-intercept: (0.5, 0); y-intercept: (0, ) 6. Non-permissible (s) Feature exhibited at each nonpermissible Behaviour near each nonpermissible y x x x 9 y x x point of discontinuity approaches, y approaches. x x x 9 approaches, y becomes very large. 7. a) C; Example: In factored form, the rational function has two non-permissible s in the denominator, which do not appear in the numerator. Therefore, the graph with two s is the most appropriate choice. B; Example: In factored form, the rational function has one non-permissible that appears in both the numerator and denominator, and another nonpermissible that is only in the denominator. Therefore, the graph with one and one point of discontinuity is the most appropriate choice. c) A; Example: In factored form, one non-permissible appears in the numerator and denominator. Therefore, the graph has a point of discontinuity, but no. Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4
x x or y x x 6 x x x x or y x 4 y x x x 4 or y x 4 c) y 4 x 4 x 6 x x 5 or y x 5 d) y x x 5 x 8 x 5 8. a) y 9. Example: y ( x 5) ( x )( x 5) BLM 9 4 Section 9. Extra Practice. a) x 5 x and x 6 c) x 0.5 and x x 5 c) x 4 d) x 4. a) x 0 and x 4 x 7 and x c) x 0 and x d) x and x. a) x 5 and x c) The of the function is 0 when the of x is or 5. The x-intercepts of the graph of the function are the same as the roots of the corresponding equation. 4. a) x 0 and x.5 5. a) 0 x 8x x and x 6 Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4
6 x y x BLM 9 6 Chapter 9 Test. D. B. C 4. D 5. C 6. A 7. C 8. B 9. a) x 6. a) x 0.76 and x 5.4 x.79 and x.79 c) x 0.5 and x 4.87 7. a) x 0.6 domain: {xx, x R}; range: {yy 0,, y R}; 4 vertical : x ; horizontal : y 0 c) As x becomes very large, y approaches 0. 0. a) x-intercept ; y-intercept 0.6 c) x d) The root of the equation is the same as the x-intercept.. a) B A c) C. a) x x 0.85 and x 6.5 8. The solution n is a non-permissible, so there is no solution. 9. Carmen: 6 h; James: 45 h Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4
. a) g(x) = f (x ) + gx ( ) x c) a vertical translation units up and a horizontal translation unit right 4. a) Example: x x 5 Method : Graph y (x ), and x 4 determine the x-intercepts of the graph. 5 Method : Graph y x x and y (x ), x 4 and determine the x-coordinates of the points where the two graphs intersect. Nonpermissible Behaviour near nonpermissible End behaviour Domain Range Equation of vertical Equation of horizontal f( x) x x 0 x approaches 0, y becomes very large. As x becomes very large, y approaches 0. {x x 0, x R} {y y 0, y R} x 0 x y 0 y x gx ( ) x approaches, y becomes very large. As x becomes very large, y approaches. {x x, x R} {y y, y R} x and x 6000 5. a) l w 6000 6000 change in l w w 6000 w w c) w 4 cm 6. a) domain: {vv > 5, v R}; range: {tt > 0, t R} c) v 5 km/h Copyright 0, McGraw-Hill Ryerson Limited, ISBN: 978-0-07-07887-4