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

Find the vector that translates the point $(1,5)$ to the point $(-1,7).$

$F$ is the point $(5,7)$. The vector that maps $F$ onto the point $G$ is $( - 1 3 )$.

Find the coordinates of $G$.

(...................... , ......................)

$P$ is the point $(-3,6)$. $Q$ is the point $(0,2)$.

Find the translation vector that maps the point $P$ onto the point $Q$.

$( 7 , 13 )$ is a point on the graph $y = \mathrm{f} ( x )$.

Write down the coordinates of a point which must be on the graph of $y = \mathrm{f} ( x ) - 2$.

A curve with equation $y=f(x)$ is translated so that the point at $(0,0)$ is mapped to the point $(0,-5)$.

Find the equation of the translated curve.

The diagram shows a sketch of the graph of $y = \mathrm{j} ( x )$.

On the same diagram, sketch the graph of $y = \mathrm{j} ( x + 2 ).$

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$y=f(x)$is translated so that the point at $(0,0)$ is mapped onto the point $(4,0)$.

(i) Find the translation vector.

(ii) Find the equation of the translated curve.

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

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

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

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

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 $y=ax^{2}+bx+c.$

The graph of $y = \cos ( x - 35 )$ for $0^{\circ}\leq x\leq360^{\circ}$ crosses the $x$-axis at two points.

Write down the coordinates of the points where this occurs.

A curve with equation $y=f(x)$ has one minimum point at $P(3,---4)$.

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

Extract:

A curve with equation y = f(x) has one minimum point at P(3, -4).

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

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 $y=f(x).$

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

Determine the value of $a$.

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

Determine the value of $b$.

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

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

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