Topical Revision Paper 7 Unit 7 Graph Transformations

Topical Revision Paper 7 Term 2 Unit 7: Graph Transformations Question 1: (i) Sketch the graphs of lnyx and xye on the same axes. [2] (ii) Describe using geometrical transformations how you would obtain the graphs of (a) 2lnyx from lnyx [1] (b) 2 xye  from xye [2] Solution: (i) (ii) (a) 2ln 2lny x y x   . Stretch graph of lnyx by a scale factor of 2 parallel to the y-axis (iii) (b) Step 1: Reflect the graph of xye about y-axis to obtain xye  . Step 2: Translate the graph of xye  in the positive y-direction by 2 units to obtain 2 xye  . Question 2: A graph with equation 3 3yx  undergoes the following two successive transformations. I A translation of 3 units in the positive y direction, II A stretch parallel to the y -axis with a scale factor of 2 . Find the equation of the resultant graph  gyx . [2] Solution: I : 3 3 33 6 yx yx     

II : 3 3 2( 6) 2 12 yx yx      3( ) 2 12g x x   Question 3: Given that f( ) lnxx and  g( ) 2ln 3xx , describe the transformation of the graph of f( )x to the graph of g( )x in two successive steps. [2] Solution: Step 1: Translate the graph of lnyx in the negative x-direction by 3 units to obtain ln( 3)yx Step 2: Stretch the graph of ln( 3)yx by a scale factor of 2 parallel to y-axis to obtain 2ln( 3)yx . Question 4: Given that the graph of 5 xye  is drawn, find the equation of the straight line to be drawn to obtain the solution to the equation ( 2) 5 xxe . [2] Solution: ( 2) 5 52 2 x x xe x e yx    Question 5: The diagram below shows partially the graph of a function f which is symmetrical about the y-axis. The points A, B and C lie on the graph. (a) Write down the new coordinates of C under the transformation 3 ( )y f x . (b) Sketch the graph of ( 2)y f x , and label clearly the new coordinates of A, B and C. x y ()y f x B ( 3,2)A  (1, 2)C 

Solution: (a) : (1, 6)newC  (b) : ( 3, 2) : ( 5, 2)new A A    : 3, 2 : (1, 2)new B B : (1, 2) : ( 1, 2)new C C   newA newB newC