Graph transformations

22The equation of circle A is x² + y² = 25 Circle A is translated by the vector 02 to give circle B. Sketch circle B. Show the coordinates of the centre of circle B and the points where circle B meets the y-axis.

Here is the graph of y = f (x)

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

Here is a sketch of the graph of y = sinx°

The point marked P is a turning point on the graph. The graph of y = sinx° is translated to give the graph of y = sin (x + 180)° + 4 Following the translation the point P, shown on the graph above, moves to point R.

Find the coordinates of R.

The graph of y = g(x) is shown on the grid.

On the grid, draw the graph of y = g(–x) + 2

The turning point on the graph of y = g(x) has coordinates (–3, 6)

Write down the coordinates of the turning point on the graph of y = g(x – 7)

The graph of y = f(x) is shown on the grid.

On the grid, sketch the graph of y = f(–x) + 3

Here is the graph of y = f(x)

On the grid below, draw the graph of y = f(x) – 4

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

The graph of y = f(x) is shown on the grid below.

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

On this grid, graph A has been reflected to give graph B. The equation of graph A is y = g(x)

Write down an equation of graph B.

The graph of y = f (x) is shown on the grid below.

On the grid above, sketch the graph of y = f (−x) Here is a sketch of the graph of y = tanx°

The graph of y = tanx° is translated to give the graph of y = g(x) Following the translation the point Q, shown on the graph above, moves to point R. Point R has coordinates (90, −5)

Find an expression for g(x) in terms of x.

18Here is a graph of y = sin x for 0 ≤ x 360

Using this graph, find estimates of all four solutions of

The graph of y = sin x is reflected in the x‑axis.

Write down an equation of the reflected graph.

Here is a graph of y = f(x)

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

The graph of the curve with equation y = f(x) is shown on the grid below.

On the grid above, sketch the graph of the curve with equation y = f(–x)

The curve C with equation y = 5 + 2x – x² is transformed by a translation to give the curve S such that the point (1, 6) on C is mapped to the point (4, 6) on S.

Find an equation for S.

The graph of y = f(x) is shown on the grid.

Point A (–2, 1) lies on the graph of y = f(x).

When the graph of y = f(x) is transformed to the graph with equation y = f(– x), point A is mapped to point B.

Write down the coordinates of point B.

The graph of the curve C with equation y f(x) is transformed to give the graph of the curve S with equation y f(x) 3 The point on C with coordinates (7, 2) is mapped to the point Q on S. Find the coordinates of Q.

The graph of y = f(x) is shown on the grid below.

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

On the grid, graph A has been reflected to give graph B.

The equation of graph A is y = g(x)

Write down the equation of graph B.

Here is the graph of y = sin xƒ for −180 x ≤ 180

On the grid, sketch the graph of y = sin xƒ – 2 for −180 ≤ x ≤ 180

The equation of a curve is y = a^x A is the point where the curve intersects the y-axis.

State the coordinates of A.

The equation of circle C is x² + y² = 16

Draw a sketch of circle B.

Label with coordinates the centre of circle B and any points of intersection with the x-axis.