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Consider the rational function g(x)=x−cax+b where a,b,c∈Z and x=c. The graph of y=g(x) is shown in the diagram below.
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Write down
the value of a,
The value of c.
Find the value of b.
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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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Consider the rational function f(x)=kx+5ax+b, for x=−k5, where a,b,k∈Z. The graph of y=f(x) has asymptotes at y=5 and x=35, and passes through the point Q(2,25).
Find the values of a,b and k.
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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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