WMA11 Jan 2019

8. WMA11/01 Edexcel IAL P1 JAN 2019, Q8 (Graphs and Transformations)

The curve C with equation y = f( x ) is shown in Figure 4.​​ 

The curve C​​ 

• has a single turning point, a maximum at​​ (4, 9)​​ 

• crosses the coordinate axes at only two places, (−3, 0) and (0, 6)​​ 

• has a single asymptote with equation y = 4 as shown in Figure 4.​​ 

(a) State the equation of the asymptote to the curve with equation y =  f(− x ).​​ 

(1)​​ 

​​ (b) State the coordinates​​ of the turning point on the curve with equation​​ y=f14x

(1)​​ 

Given that the line with equation y = k, where k is a constant, intersects C at exactly one point,​​ 

(c) state the possible values for k.​​ 

(2)​​ 

k=9,  k≤4

The curve C is transformed to a new curve that passes through the origin.​​ 

(d)

• Given that the new curve has equation y = f( x ) − a , state the value of the constant a.​​ 

• Write down an equation for another single transformation of C that also passes through the origin.​​ 

(2)

fx-3

SOLUTION​​ 

a-​​ The graph of y=f(-x) is a​​ reflection of the graph of y=f(x) in the y-axis. This means that the sign of y-cordinates only changes. There will be no effect on the horizpontal asymptote equation. Hence, the equation of asymptote would be​​ 

y=4

b-​​ The graph of​​ y=f14x​​ is the strech of f(x) by the scale factor of ¼ in the horizontal, direction. Therefore, the x-cordinate of turning point be 1/(1/4) ​​ of the value it has on y=f(x) graph.

Hence, the coordinate of​​ 

16,9

c-​​ 

k=9,  k≤4

d-​​ 

i-​​ Since the new curve has the y = f( x ) − a, the transformation under which y=f(x) has undergone is translation by ‘a’​​ units in downward direction.

Hence, only possible translation is when the graph is translated by 6 units downwards.​​ 

d- ii-​​ Another possible translation which would make the new curve pass through the origin may be when the curve y=f(x) is translated towards the left by 3 units.​​ 

Hence, the equation would be​​ 

fx-3