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

Write down the equation of the line of symmetry of the graph with equation $y=\left(x-2\right)\left(x+2\right)$.

On the diagram, sketch the graph of $y=\left(x+1\right){\left(x-3\right)}^2$.

Label the values where the graph meets the $x$-axis and the $y$-axis.

Sketch the graph of the function.

$y=\frac{1}{x}$

The diagrams A, B, C, D, E and F are six graphs of different functions.

Complete the table to identify the correct graph for each function. One has been done for you. 

$\mathrm{f}\left(x\right)=x(x+2)(x–3)$

On the diagram, sketch the graph of $y=\mathrm{f}\left(x\right)$for $–3⩽x⩽4$.
Show the values of the intersections with the axes. 

The curve $C$ has equation $y={\left(x-3\right)}^2-5$

Using the axes below, sketch the curve $C$.
On your sketch show clearly

(i) the exact coordinates of any points of intersection of $C$ with the coordinate axes,

(ii) the coordinates of the turning point.

Here are six graphs.

Complete the table below with the letter of the graph that could represent each given equation.

Write your answers on the dotted lines.

The curve$\mathit{C}$has equation $y=4{(x-1)}^2-a$   where $a>4$

Using the axes below, sketch the curve $\mathit{C}$.
On your sketch show clearly, in terms of $a$,

(i) the coordinates of any points of intersection of $\mathit{C}$ with the coordinate axes,

(ii) the coordinates of the turning point.