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Exam-Style Questions on Transformation of GraphsProblems on Transformation of Graphs adapted from questions set in 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 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?
3. | 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.
4. | IB Standard |
Let \(f(x) = {x^2}\) and \(g(x) = 3{(x+2)^2}\) .
The graph of \(g\) can be obtained from the graph of \(f\) using two transformations.
(a) Give a full description of each of the two transformations.
(b) The graph of \(g\) is translated by the vector \( \begin{pmatrix}-4\\5\\ \end{pmatrix}\) to give the graph of \(h\).
The point \(( 2{\text{, }}-1)\) on the graph of \(f\) is translated to the point \(P\) on the graph of \(h\).
Find the coordinates of \(P\).
5. | IB Standard |
Let \(f\) and \(g\) be functions such that \(g(x) = 3f(x - 2) + 7\) .
The graph of \(f\) is mapped to the graph of \(g\) under the following transformations: vertical stretch by a factor of \(k\) , followed by a translation \(\left( \begin{array}{l} p\\ q \end{array} \right)\) .
Write down the value of:
(a) \(k\)
(b) \(p\)
(c) \(q\)
(d) Let \(h(x) = - g(2x)\) . The point A(\(8\), \(7\)) on the graph of \(g\) is mapped to the point \({\rm{A}}'\) on the graph of \(h\) . Find \({\rm{A}}'\)
6. | IB Standard |
Two functions are defined as follows: \(f(x) = 2\ln x\) and \(g(x) = \ln \frac{x^2}{3}\).
(a) Express \(g(x)\) in the form \(f(x) - \ln a\) , where \(a \in {{\mathbb{Z}}^ + }\) .
(b) The graph of \(g(x)\) is a transformation of the graph of \(f(x)\) . Give a full geometric description of this transformation.
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