Transformations of Graphs (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

The graph with equation undergoes a translation of 3 units to the right.

Show that the equation of the translated graph simplifies to

A curve with equationis translated so that the point at is mapped onto the point .

(i) Find the translation vector.

[1]

(ii) Find the equation of the translated curve.

[1]

The diagram shows part of the curve with equation .
The coordinates of the minimum point of this curve are

Write down the coordinates of the minimum point of each of the curves below:

(i)

[1]

(ii)

[1]

The graph with equation undergoes a translation of one unit in the negative direction and five units in the positive direction.

Find the equation of the translated graph.
Give your answer in the form

The graph of for crosses the -axis at two points.

Write down the coordinates of the points where this occurs.

A curve with equation  has one minimum point at .

Write down the coordinates of the minimum point of the curve with the equation  .

Write down an equation of the graph if the minimum point is instead translated to the point

The graph with equation undergoes a translation of two units in the positive direction and four units in the negative direction.

The equation of the translated graph is

Find the values of and .