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Access custom-built, exam-style problems for transformations & asymptotes. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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Consider the rational function g(x)=3+2x7−4x, for x=−23.
For the graph of y=g(x) find
the coordinates of the axes intercepts,
the equations of the asymptotes.
Hence sketch the graph of y=g(x) on the axes below.
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The graph of y=g(x) is shown in the following for −3≤x≤5.
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Write down the value of g(3)
Find the value of
(g∘g)(5)
(g−1∘g−1)(1)
Sketch the graph of y=g(x+1)−1 on the axes above.
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The following diagram shows the graph of a function f.
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On the axes above, sketch the graph of y=2f(x+3)−1, indicating clearly the point A′ corresponding to point A.
Consider a function g defined by g(x)=af(x)+b. The graph of g can be obtained from the graph of f by
A vertical translation of 2 units followed by
A vertical stretch with scale factor 3.
Find the value of a and the value of b.
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The graph of y=g(x), for −3≤x≤3, is shown in the following diagram.
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Write down the value of
g(−2)
g−1(2)
g∘g(0)
Sketch the graph of y=−g(−x) on the graph above.
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