The curve with equation is translated so that the point at (0, 0) is mapped onto the point (4, 0).
Find an equation of the translated curve.
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The curve with equation is translated so that the point at (0, 0) is mapped onto the point (4, 0).
Find an equation of the translated curve.
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The graph of is shown on both grids below.
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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 the curve with equation
[1]
[1]
[1]
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The graph of is shown on the grid.
The graph G is a translation of the graph of .
Write down, in terms of f, the equation of graph G.
The graph of has a maximum point at (-4, 3).
Write down the coordinates of the maximum point of the graph of
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The diagram shows a sketch of the curve with equation
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
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Here is the graph of
On the grid above, draw the graph of
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The curve with equation is transformed to the curve with equation by the single transformation
Describe fully the transformation
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On the axes, sketch the curve
You must show the coordinates of the -intercept.
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One of these is the graph of for
Circle the letter above the correct graph.
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(7, 28) is a point on the graph
Circle the point which must be on the graph
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The diagram shows part of the curve with equation .
The coordinates of the maximum point of the curve are (3, 5).
Write down the coordinates of the maximum point of the curve with equation
The curve with equation is transformed to give the curve with equation
Describe the transformation.
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The diagram shows a sketch of the graph of
Write down the coordinates of the point .
On the same diagram, draw a sketch of the graph of
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Here is the graph of for
On the grid, sketch the graph of for
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Here is the graph of for
On the grid above, sketch the graph of for
Here is the graph of for
On the grid above, sketch the graph of for
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The equation of a curve is
is the point where the curve intersects the -axis.
State the coordinates of .
The equation of circle is
The circle is translated by the vector to give circle .
Draw a sketch of circle .
Label with coordinates
the centre of circle
and any points of intersection with the -axis.
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The graph of is shown on the grids.
On this grid, sketch the graph of
On this grid, sketch the graph of
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The graph of is shown on the grid.
On the grid above, sketch the graph of .
The graph of is shown on the grid.
The graph G is a translation of the graph of
Write down the equation of graph G.
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Here is the graph of for
In parts (a) and (b) the graph of is shown as a dashed line.
On the grid below, draw the graph of for
On the grid below, draw the graph of
Rita tries to draw the graph of for
Here is her graph.
Give a reason why Rita’s graph is incorrect.
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Here is a sketch of
The curve passes through the points
(–2, –10) (–1, –3) (0, –2) (1, –1) (2, 6)
On the grid, sketch the curve
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The curve with equation is reflected in the -axis.
Circle the equation of the reflected curve.
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The graph of for crosses the -axis in two places.
Write down the values of where this occurs.
...........................
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Sketch the graph of for .
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The graph of is shown on each of the grids.
On this grid, sketch the graph of
On this grid, sketch the graph of
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The graph of is shown on both grids below
On the grid above, sketch the graph of
On this grid, sketch the graph of
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This is a sketch of the curve with the equation
The only minimum point of the curve is at .
Write down the coordinates of the minimum point of the curve with the equation
Write down the coordinates of the minimum point of the curve with the equation
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The graph of , where is a positive constant, is shown above.
Find the value of .
The graph of for values of from is shown above.
On the same axes, draw the graph of for values of from
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The graph of is transformed to give the graph of
The point on the graph of is mapped to the point on the graph of
The coordinates of point are
Find the coordinates of point .
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The graph of the curve with equation is transformed to give the graph of the curve with equation
The point on with coordinates is mapped to the point on .
Find the coordinates of .
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The graph of intersects the -axis at two points.
The coordinates of the two points are (–1, 0) and (6, 0)
The graph of passes through the point with coordinates (2, 0), where is a constant.
Find the two possible values of .
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The curve has equationwhere
The curve has equation where
By writing in the form , where and are constants,
describe fully a series of transformations that map the curve onto the curve .
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The curve has equation where
The point is the maximum point on .
Write down the coordinates of .
The curve is transformed to the curve by a translation of
Find an equation for the curve .
The curve is transformed to the curve .
The curve has equation
Describe fully the transformation that maps curve onto curve .
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The graph of for is drawn on the grid below.
Find the value of , the value of and the value of .
a = .......................................................
b = .......................................................
c = .......................................................
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The equation of a curve is
The curve is transformed to curve under the translation
Find an equation of curve .
You do need to simplify the equation.
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The graph of is translated 4 units to the right.
The translated graph has equation
Work out .
Give your answer in the form where and are integers.
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Curve has equation
Curve is a reflection in the -axis of curve .
Work out the equation of curve .
Give your answer in the form where and are integers.
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For all values of
On the grid, draw the graph of the composite function for
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