Cambridge International AS & A Level Mathematics: Pure Mathematics 1
y
2 The diagram shows the graph of y = f( x ).
2
Write down, in terms of f( x ), the equation of the graph of each of the following diagrams.
y = f(x)
1 –4 –3 –2 –1 O –1
1
2
3
x
–2
b
y 4
y 4 3
3
2
2
1
1 –4 –3 –2 –1 O –1
1
2
3
4 x
–4 –3 –2 –1–1O
3 2 1 1
2
3
4 x
SA M
–3
4 x
PL
y 4
–2
3
–4
–4
64
2
–3
–3
–4 –3 –2 –1–1O
1
–2
–2
c
E
a
–4
3 Given that y = x 2 find the image of the curve y = x 2 after each of the following combinations of transformations: a a stretch in the y-direction with factor 3 followed by a translation by the 1 vector 0 1 b a translation by the vector followed by a stretch in the y-direction with 0 factor 3.
4 Find the equation of the image of the curve y = x 2 after each of the following combinations of transformations and in each case sketch the graph of the resulting curve: a a stretch in the x-direction with factor 2 followed by a translation by the 5 vector 0 5 b a translation by the vector followed by a stretch in the x-direction with 0 factor 2.
c On a graph show the curve y = x 2 and each of your answers to parts a and b.
Original material © Cambridge University Press 2017