WMA11 June 2022

• WMA11/01 Edexcel​​ IAL, P1, June 2022, Q4 (Transformations of Graphs:​​ Translations, Reflections)

Figure 1 shows a sketch of a curve with equation y = f(x)​​ 

The curve has a minimum​​ at P(−1, 0) and a maximum at​​ Q32,2

The line with equation y = 1 is the only asymptote to the curve.​​ 

On separate diagrams sketch the curves with equation​​ 

• y = f(x) − 2​​ 

(3)

• y = f(−x)​​ 

(3)​​ 

On each sketch you must clearly state​​ 

• the coordinates of the maximum and minimum points​​ 

• the equation of the asymptote

SOLUTION​​ 

i-  ​​​​ y = f(x) − 2

In case of this part, the graph translates 2 units downwards. Therefore, the y-coordinates of all the points marked on the f(x) graph is subtracted by 2​​ units.​​ 

The translation vector is given as​​ 

0-2

The points on​​ fx​​ were​​ P-1, 0& Q32, 2. After translation, the graph of​​ fx-2 has the points​​ P'-1, -2& Q32, 0. Similarly, the equation of asymptote will be y=-1.​​ 

ii- ​​ y = f(−x)

In case of this part, the graph reflects in the y-axis. Therefore, the​​ sign of x-coordinates of all the points marked on the f(x) graph is swapped.​​ 

The points on​​ fx​​ were​​ P-1, 0& Q32, 2. After translation, the graph of​​ f-xhas the points​​ P'1,0& Q-32, 2. Similarly, the equation of asymptote remains to be y=1.​​