The point lies on the curve with equation .
State the coordinates of the image of point on the curves with the following equations:
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The point lies on the curve with equation .
State the coordinates of the image of point on the curves with the following equations:
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The point lies on the curve with equation .
State the coordinates of the image of point on the curves with the following equations:
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The point lies on the curve with equation
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The diagram below shows the graph of The two marked points and lie on the graph.
In separate diagrams, sketch the curves with equation
On each diagram, give the coordinates of the images of points and under the given transformation.
On the graph of the image of one of the two marked points has an coordinate of 2. Find the two possible values of .
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The diagram below shows the graph of . The marked point lies on the graph, and the graph meets the origin at the marked point .
In separate diagrams, sketch the curves with equation
On each diagram, give the coordinates of the images of points and under the given transformation.
On the graph of the image of one of the two marked points has a coordinate of 4. Find the value of .
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The diagram below shows the graph of . The graph intersects the coordinate axes at the two marked points and . The graph has two asymptotes as shown, with equations and
In separate diagrams, sketch the curves with equation
(i)
(ii)
On each diagram, give the coordinates of the images of points and under the given transformation, as well as stating the equations of the transformed asymptotes.
The graph of has an asymptote at one of the coordinate axes. Find the value of .
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Describe, in order, a sequence of transformations that maps the graph of onto the following graphs:
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Given that find an expression for , where is obtained by applying the following sequence of transformations to .
Translation by
Vertical stretch of scale factor 4
Translation by
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Find an expression for .
Find an expression for .
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The equation , where , with , is shown below.
The points and are the points where the graph intercepts the coordinate axes.
Write down, in terms of , the coordinates of and .
Sketch the graph of , labelling the images of the points and stating their coordinates in terms of .
Write down the value of a such that the point is three times as far from the origin as the point .
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The function is to be transformed by a sequence of functions, in the order detailed below:
A horizontal stretch by scale factor 2
A reflection in the -axis
A translation by
Write down an expression for the combined transformation in terms of .
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The diagram shows the graph of , where ,
Write down the maximum value of when .
Write down the minimum value of when .
Write down the first value of for which this minimum occurs.
Find, in terms of , the combination of transformations that would map the graph of onto the graph of , .
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Let .
Write down the value of .
The function f can be written in the form of.
Find the values of a, h and k.
The graph of g is obtained from the graph of f by a reflection in the x-axis followed by a translation by the vector .
Find, giving your answer in the form of
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