Transformations of Graphs Practice Questions

Write down the coordinates of the maximum point of the curve with equation $y=f(x)-3$.

Write down the coordinates of the two points where the curve with equation $y=f(x+2)$ crosses the $x$-axis.

The graph of $y=\cos x^\circ$ is translated by the vector $\begin{pmatrix}0\\4\end{pmatrix}$.

Write down an equation of the translated graph.

The graph of $y=\sin x^\circ$ is translated $90$ units in the negative $x$-direction.

Write down an equation of the translated graph.

On the grid, sketch the graph of $y=f(x)-3$.

On the grid, sketch the graph of $y=f(x-1)$.

Write down the equation of graph $B$.

Write down the coordinates of the minimum point of the graph with equation $y=f(x+4)$.

Describe fully the single transformation that maps the graph of $y=\cos x^\circ$ onto the graph of $y=\cos (x+90)^\circ$.

Hence write down an equation of the graph of $y=\cos (x+90)^\circ$ in terms of $\sin x^\circ$.

$C$ is translated by the vector $\begin{pmatrix}0\\3\end{pmatrix}$ to give the curve $S$.

Write down an equation of $S$.

$C$ is translated $2$ units in the negative $x$-direction to give the curve $T$.

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

Write down the coordinates of the turning point of $T$.

Write down the coordinates of the turning point of $D$ and state whether it is a maximum point or a minimum point.

The point $R$ on $C$ is mapped to the point $R'$ on $D$.

Find the coordinates of $R'$.

Show that $D$ has equation $y=2x^{2}-4x-5$.