Transformations of Graphs (OCR GCSE Maths: Higher): Exam Questions

The diagram shows a sketch of the graph of $y=\cos x.$

Write down the coordinates of the point $A$.

On the same diagram, draw a sketch of the graph of $y=-\cos x.$

Here is the graph of $y=\sin x^{\circ }$ for  $-180⩽x⩽180$

On the grid, sketch the graph of $y=\sin x^{\circ }-2$ for $—180⩽x⩽180$

Here is the graph of $y=\sin x^{\circ }$ for  $-180⩽x⩽180$

On the grid above, sketch the graph of $y=\sin x^{\circ }+2$ for $—180⩽x⩽180$

Here is the graph of $y=\cos x^{\circ }$ for  $-180⩽x⩽180$

On the grid above, sketch the graph of $y=-\cos x^{\circ }$ for $—180⩽x⩽180$

The graph of $y=\cos \left(x-30\right)$ for  $0°⩽x⩽360°$ crosses the $x$-axis in two places.

Write down the values of $x$ where this occurs.

$x=$...........................

Sketch the graph of $y=-\sin x$ for $0°⩽x⩽360°$.

Here is the graph of $y=\cos x$for $0°⩽x⩽360°$

In parts (a) and (b) the graph of $y=\cos x$ is shown as a dashed line.

On the grid below, draw the graph of $y=\cos (x–90°)$ for $0°⩽x⩽360°$

On the grid below, draw the graph of $y=1+\cos x\mathrm{for}0°⩽x⩽360°$

Rita tries to draw the graph of$y=\cos (–x)$ for$0°⩽x⩽360°$
Here is her graph.

Give a reason why Rita’s graph is incorrect.

The curve with equation   $y=x^2-5x+2$ is reflected in the $x$-axis.

Circle the equation of the reflected curve.

The graph of $y=k^x$, where $k$ is a positive constant, is shown above.

Find the value of $k$.

The graph of $y=\sin x^{\circ }$ for values of $x$ from $—270\mathrm{to}+270$ is shown above.

On the same axes, draw the graph of $y=1-\sin x^{\circ }$ for values of $x$ from $—270\mathrm{to}+270$

The equation of a curve is $y=a^x$
$A$ is the point where the curve intersects the $y$-axis.

State the coordinates of $A$.

The equation of circle $\mathbf{C}$ is $x^2+y^2=16$

The circle $\mathbf{C}$ is translated by the vector $\left(\begin{array}{c}3\\ 0\end{array}\right)$ to give circle $\mathbf{B}$.

Draw a sketch of circle $\mathbf{B}$.

Label with coordinates   
 the centre of circle $\mathbf{B}$    
and any points of intersection with the $x$-axis.

The curve $C$ has equation  $y=9–3{(x+2)}^2$

The point $A$ is the maximum point on $\mathbf{C}$.

Write down the coordinates of $A$.

The curve $\mathbf{C}$ is transformed to the curve $\mathbf{S}$ by a translation of $\left(\begin{array}{c}4\\ 0\end{array}\right)$
Find an equation for the curve $\mathbf{S}$.

The curve $\mathbf{C}$ is transformed to the curve $\mathbf{T}$.
The curve $\mathbf{T}$ has equation $y=3{(x+2)}^2–9$

Describe fully the transformation that maps curve $\mathbf{C}$ onto curve $\mathbf{T}$.

The graph of$y=a\cos (x–b)°+c$ for $-180⩽x⩽360$is drawn on the grid below.

Find the value of $a$, the value of $b$ and the value of $c$.

a = ....................................................... 

= ....................................................... 

   c = ....................................................... 

The equation of a curve $\mathbf{C}$is $y=x^2+3x+4$

The curve $\mathbf{C}$is transformed to curve $\mathbf{S}$under the translation $\left(\begin{array}{c}4\\ 6\end{array}\right)$

Find an equation of curve $\mathbf{S}$.

You do need to simplify the equation.

Curve $\mathrm{P}$ has equation $y=2{(x–1)}^2–5$

Curve $\mathrm{Q}$ is a reflection in the $y$-axis of curve $\mathrm{P}$.

Work out the equation of curve $\mathrm{Q}$.

Give your answer in the form    $y=a{x}^2+bx+c$     where $a,b$ and $c$ are integers.