WMA11 October 2022

7. WMA11/01 Edexcel IAL P1 October 2022, Q7 (Graphs & Transformations)

Figure 1 shows the curve with equation y = f(x).​​ 

The points P(–4, 6), Q(–1, 6), R(2, 6) and S(3, 6) lie on the​​ curve.​​ 

(a) Using Figure 1, find the range of values of x for which​​ 

f(x) < 6

(3)

(b) State the largest solution of the equation​​ 

f(2x) = 6

(1)

(c)

(i) Sketch the curve with equation y = f(–x).​​ 

On your sketch, state the coordinates of the points to which​​ P, Q, R and S are transformed.​​ 

(ii) Hence find the set of values of x for which​​ 

f–x≥ 6 and x < 0 

(4)

SOLUTION

a- ​​ 

x<-4,-1<x<2,    x<3

b-​​ 

The largest solution of​​ fx=6​​ is​​ 

x=3

So, on observing that​​ 

f3=6

And than comparing with​​ 

f2x=6

The value of x is​​ 

2x=3

x=32

c-i-​​ 

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​​ (-4, 6),​​ (-1, 6), (2, 6), and(3,6). After translation, the graph of​​ f-xhas the points​​ (+4, 6),​​ (+1, 6), (-2, 6), and (-3,6).

c-ii-

-3≤x≤-2