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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
The graph of the curve A with equation \(y=f(x)\) is transformed to give the graph of the curve B with equation \(y=5-f(x)\).
The point on A with coordinates (3, 9) is mapped to the point W on B.
Find the coordinates of W.
2. | GCSE Higher |
The graph of the curve with equation y = \(f(x)\) is shown on the grid below.
(a) On the grid above, sketch the graph of the curve with equation \(y = f(–x)\)
The red curve with equation \(y = x^2-5x+4\) is transformed by a translation to give the blue curve such that the point (2.5, -2.25) on the red curve is mapped to the point (-2.5, -2.25) on the blue curve.
(b) Find an equation for the blue curve.
3. | GCSE Higher |
The graph of the following equation is drawn and then reflected in the x-axis
$$y = 2x^2 - 3x + 2$$(a) What is the equation of the reflected curve?
The original curve is reflected in the y-axis.
(b) What is the equation of this second reflected curve?
4. | IB Standard |
\(f\) and \(g\) are two functions such that \(g(x)=3f(x+2)+7\).
The graph of \(f\) is mapped to the graph of \(g\) under the following transformations:
A vertical stretch by a factor of \(a\) , followed by a translation \(\begin{pmatrix}b \\c \\ \end{pmatrix}\)
Find the values of
(a) \(a\);
(b) \(b\);
(c) \(c\).
(d) Consider two other functions \(h\) and \(j\). Let \(h(x)=-j(2x)\). The point A(8, 7) on the graph of \(j\) is mapped to the point B on the graph of \(h\). Find the coordinates of B.
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