Transformations of Graphs (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

The graph with equation $y=x^2+2$ undergoes a translation of 3 units to the right.

Show that the equation of the translated graph simplifies to $y=x^2-6x+11.$

A curve with equation$y=\mathrm{f}\left(x\right)$is translated so that the point at $(0,0)$ is mapped onto the point $(4,0)$.

(i) Find the translation vector.

[1]

(ii) Find the equation of the translated curve.

[1]

The diagram shows part of the curve with equation $y=\mathrm{f}\left(x\right)$.
The coordinates of the minimum point of this curve are $\left(3,-4\right)$

Write down the coordinates of the minimum point of each of the curves below:

(i) $y=\mathrm{f}\left(x\right)+3$

[1]

(ii) $y=\mathrm{f}\left(x+2\right)$

[1]

The graph with equation $y=x^2-4x$ undergoes a translation of one unit in the negative $x$ direction and five units in the positive $y$ direction.

Find the equation of the translated graph.
Give your answer in the form $y=a{x}^2+bx+c.$

The graph of $y=\cos \left(x-35\right)$ for $0°\le x\le 360°$ crosses the $x$-axis at two points.

Write down the coordinates of the points where this occurs.

A curve with equation $y=\mathrm{f}\left(x\right)$ has one minimum point at $P(3,—4)$.

Write down the coordinates of the minimum point of the curve with the equation  $y=\mathrm{f}\left(x-5\right)+6$.

Write down an equation of the graph if the minimum point is instead translated to the point $\left(0,0\right)$

The graph with equation $y=x^2+ax+b$ undergoes a translation of two units in the positive $x$ direction and four units in the negative $y$ direction.

The equation of the translated graph is $y=x^2-x-10.$

Find the values of $a$ and $b$.

The point $P(3,2)$ lies on the curve with equation $y=\mathrm{f}\left(x\right).$

On the graph of $y=\mathrm{f}\left(x\right)+a$, where $a$is a constant, the point $P$ is mapped to the point $(3,-5)$.

Determine the value of  $a$.

On the graph of $y=\mathrm{f}(x+b)$, where $b$is a constant, the point $P$ is mapped to the point $(-1,2)$.

Determine the value of $b$.

A different function, $\mathrm{g}\left(x\right)$, is a cubic function of the form $\mathrm{g}\left(x\right)=a{x}^3+b{x}^2+cx+d$.

The graph of $y=\mathrm{g}\left(x\right)$ is translated by the vector $\left(\begin{array}{c}5\\ 0\end{array}\right)$.

Write down the equation of the transformed graph in terms of $a,b,c,d$, and $x$.