## Exam-Style Questions on Transformation of Graphs## Problems 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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