Graph transformations

The equation of a curve is y = f (x)

There is only one minimum point on the curve. The coordinates of this minimum point are (8, –12)

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

y = f (x) + 3

y = f (2x)

The curve with equation y = f(x) has one turning point. The coordinates of this turning point are (−6, 9)

Write down the coordinates of the turning point on the curve with equation y = f (3x)

The curve C with equation y = g(x) is transformed to give the curve S with equation y = g(x + a) + b

The point (4, −5) on C is mapped to the point (1, −16) on S

Write down the value of a and the value of b

Express 2x² 11x 9 in the form a(x b)² c where a, b and c are numbers to be found.

The curve C has equation y 2(x 3)² 11(x 3) 9

The point P is the minimum point on C

Find the coordinates of P

A curve has equation y = f (x)

There is one minimum point on this curve. The coordinates of this minimum point are (5, ‒4)

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

y = f (x + 7)

y = f (x) ‒ 6

24The curve with equation f(x) = 5x² 9x 2 is transformed to the curve with equation

g(x) = 5 x 4² 9 x 4 8 by the translation b a

Write down the value of a and the value of b

The graph of y p cos x q for 0 x 360 is drawn on the grid below.

Given that p > 0 and 0 < q < 360

find the value of p and the value of q

Curve C has equation y = f (x) The graph of curve C has one maximum point. The coordinates of this maximum point are (3, 5)

Write down the coordinates of the maximum point on the curve with equation

y = 2f (x)

y = f (x) – 7

y = f (–x)

Curve L has equation y = x² + 7x + 20

Find an equation for S Give your answer in the form y = ax² + bx + c

A curve has equation y = f(x)

There is only one turning point on the curve. The coordinates of this turning point are (6, 5)

Write down the coordinates of the turning point on the curve with equation

y = f(x – 4)

y = f(3x)

20Here is a sketch of the curvey = acos(x + b) for 0 ≤ x ≤ 360

Given that 0 < b < 180

find the value of a and the value of b

The graph of y = a sin x ° + b is drawn on the grid.

Find the value of a and the value of b

The diagram shows a sketch of part of the curve with equation y = f (x)

There is one maximum point on this curve. The coordinates of this maximum point are (s, t)

Find, in terms of s and t, the coordinates of the maximum point on the curve with equation

y = f (x − 2)

y = 3f (x)

Express 2x² – 12x + 3 in the form a(x + b)² + cwhere a, b and c are integers.

The curve C has equation y = 2(x + 4)² – 12(x + 4) + 3

The point M is the minimum point on C

Find the coordinates of M

The point A with coordinates (–3, 2) lies on the straight line with equation y = f(x)

Find the coordinates of the image of the point A on the straight line with equation

y = f(x) – 3

Here is a sketch of part of the curve with equation y = g(x)

The point B with coordinates (p, q) lies on the curve.

Find the coordinates of the image of the point B on the curve with equation

y = –g(x – c)

where c is a constant.

The diagram shows a sketch of the curve with equation y = f(x)

There is only one maximum point on the curve. The coordinates of this maximum point are (5, 7)

Write down the coordinates of the maximum point on the curve with equation

y = f(x + 9)

y = f(x) + 3

A curve has equation y = f(x)

The coordinates of the minimum point on this curve are (–9, 15)

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

y = f(x + 3)

The graph of y = acos (x + b) for 0 x 360 is drawn on the grid below.

Given that a 0 and that 0 < b < 360

find the value of a and the value of b.

A curve has equation y = f(x) There is only one maximum point on the curve. The coordinates of this maximum point are (–3, 4)

Write down the coordinates of the maximum point on the curve with equation

y = f(x) – 6

y = f(2x)

The curve with equation y = g(x) is transformed to the curve with equation y = −g(x) by the single transformation T.

Describe fully the transformation T.

The diagram shows the graph of y = f(x)

On the grid, draw the graph of y = 2f(x – 1)

Find the value of a and the value of b.

Another curve C has equation y= f (x) The coordinates of the minimum point of C are (4, 5)

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

y= f (2x)

y= f (x) − 7

A curve has equation y = f(x)

There is only one maximum point on the curve. The coordinates of this maximum point are (4, 3)

Write down the coordinates of the maximum point on the curve with equation

y = f(x – 5)

y = 3f(x)

Here is the graph of y = a sin(bx)° for 0 ≤ x ≤ 360

Find the value of a and the value of b.

The graph of y = sinx° for 0 x ≤ 360 is drawn on the grid.

On the grid, draw the graph of y = 2sin(x + 30)° for 0 x ≤ 360

Write x²x + 10 in the form (xa)² + b where a and b are integers.

Hence, describe fully the single transformation that maps the curve with equation y = x² onto the curve with equation y = x²x + 10

The diagram shows the curve with equation y = f (x) The coordinates of the minimum point of the curve are (–2, –1)

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

y = f (x – 5)

The graph of y = a sin(x – b) + c for –90 x 450 is drawn on the grid below.

Find the value of a, the value of b and the value of c.

Here is the graph of y = f(x)

On the grid above, draw the graph of y = 2f(x)

Here is the graph of y = f(x)

On the grid above, draw the graph of y = f(– x)