Cambridge International Mathematics

Further functions 23 Contents: A Cubic functions [3.2, 3.3] B Inverse functions [3.9] C Using technology [2.11, 3.6] D Tangents ...

Discovery Cubic functions#endboxedheading To discover the shape of different cubics you can either use the graphing package or y ...

y -2 x 12 2 O @\=Qw_\(!\+\2)(!\-\1)(!\-2) y O 2 x @\=\2!(!-2)X ² for a cubic in the form y=a(x¡®)^2 (x¡ ̄) the graphtouchesthex- ...

a Thex-intercepts are¡ 1 , 2 , and 4 ) f(x)=a(x+ 1)(x¡2)(x¡4) But when x=0, y=¡ 8 ) a(1)(¡2)(¡4) =¡ 8 ) 8 a=¡ 8 ) a=¡ 1 So, f(x) ...

2 Find the equation of the cubic function which: a hasx-intercepts 1 and 3 , y-intercept 9 and passes through(¡ 1 ,8) b touches ...

Thehorizontal line testsays that ‘for a function to have an inverse function, no horizontal line can cut it more than once.’ Exa ...

y -3 x 3 O y x O 3 y O x y x 2 -2 O GRAPHING PACKAGE 4aExplain why the horizontal line test is a valid test for the existence of ...

Example 5 Self Tutor Consider f(x)= 3 x¡ 9 x^2 ¡x¡ 2 : a Use your graphics calculator to obtain a sketch of the function. b Stat ...

5 For these functions: i Use your graphics calculator to obtain a sketch of the function. ii State the equations of any asymptot ...

10 Consider = x+2 x¡ 1 and g(x)=2x. a Sketch the graphs of y=f(x) and y=g(x) on the same set of axes for ¡ 56 x 65 b Find the co ...

Example 6 Self Tutor Solve 2 x=4¡x by graphing y=2x and y=4¡x on the same set of axes. Give your answer correct to 3 significant ...

Atangentto a curve is a straight line whichtouchesthe curve. Oblique means at an angle to horizontal and vertical. Other curves ...

Review set 23A #endboxedheading 1 Sketch the graphs of the following cubics, showing all axes intercepts: a y=x(x¡2)(x+3) b y=¡2 ...

2 The graph alongside has the form y=x^3 +6x^2 +cx+d. Find the values ofcandd. 3 Find f¡^1 (x) for: a f(x)=8x b f(x)= 2 x¡ 1 c f ...

Vectors 24 Contents: A Directed line segment representation [5.1, 5.3] B Vector equality [5.1, 5.2] C Vector addition [5.2] D Ve ...

Consider a bus which is travelling at 100 km/h in a south east direction. A good way of representing this situation is to use an ...

2 If represents a force of 45 Newtons due east, draw a directed line segment representing a force of: a 75 N due west b 60 N sou ...

Example 2 Self Tutor ABCD is a parallelogram in which ¡! AB=a and ¡! BC=b. Find vector expressions for: a ¡! BA b ¡! CB c ¡! AD ...

DISPLACEMENT VECTORS Suppose we have three towns A, B and C. A trip from A to B followed by a trip from B to C is equivalent to ...

Example 4 Self Tutor Sonya can swim at 3 km/h in calm water. She swims in a river where the current is 1 km/h in an easterly dir ...