Question Type 4: Visually applying simple matrix transformations Exercises

Given point $A(2,1)$, apply an enlargement of scale factor 3 centred at the origin, then translate by vector $(0,3)$. Find the coordinates of the image $A'$.

A square of side length 2 is subjected to a horizontal stretch factor 3 and a vertical stretch factor 4. Compute the area of the image.

The graph of $y=f(x)$ is transformed to $y=g(x)=-2f(3x)+5$. Describe each transformation in order.

Let $f(x)=x^2$. Perform a horizontal stretch by factor $\tfrac12$, then a vertical stretch by factor 4. Write down the equation of the transformed function $g(x)$.

A function $f(x)$ is first subjected to a vertical stretch by factor 5 about the $x$‐axis, then a horizontal stretch by factor 2 about the $y$‐axis. Write the equation of the resulting function in terms of $f$.

The function $f(x)=1/x$ is mapped to $h(x)=-\tfrac1x+2$. Describe the sequence of transformations that takes $f$ to $h$.

Triangle $ABC$ has vertices $A(1,2)$, $B(3,1)$ and $C(2,4)$. Reflect it in the $y$‐axis, then enlarge by factor 2 about the origin. Find the coordinates of $A'$, $B'$, $C'$.

Determine the single $2\times2$ matrix representing first an enlargement by factor 2 about the origin, then a reflection in the line $y=0$.

Find the $2\times2$ matrix representing first a horizontal stretch by factor 3, then a vertical stretch by factor 2 in the plane.

The mapping $T:(x,y)\mapsto(3x+1,\,3y-2)$.
(a) Describe $T$ as an enlargement followed by a translation.
(b) Describe $T$ as a horizontal stretch, a vertical stretch, and translations.

A function $f(x)$ is transformed to $g(x)=9f(2x-4)+3$. List, in order, the sequence of transformations applied to $f(x)$ to obtain $g(x)$.

A rectangle has vertices $(1,1),(4,1),(4,3),(1,3)$. Reflect it in the line $x=2$, then apply a vertical stretch by factor 2. Find the final coordinates.