Graphs of Functions (Edexcel IGCSE Maths): Exam Questions

Brogan needs to draw the graph of $y=x^{2}+1$

Here is her graph.

Write down one thing that is wrong with Brogan's graph.

Complete the table of values for $y=x^{3}---4x$

On the grid, draw the graph of $y=x^{3}---4x$ from $x=-3\mathrm{to}x=3$

Complete the table of values for $y=x^{3}---3x+1$

On the grid, draw the graph of $y=x^{3}---3x+1$ for values of $x$ from $---2\mathrm{to}2$

Complete the table of values for $y=\frac{6}{x}$

On the grid, draw the graph of $y = \frac{6}{x} \text{for} 0.5 less-than \text{or} \text{slanted} \text{equal} \text{to} x less-than \text{or} \text{slanted} \text{equal} \text{to} 6$

Complete the table of values for $y=\frac{4}{x}$

On the grid, draw the graph of $y=\frac{4}{x}$ for $0.5 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 8$

The graph of $y=f(x)$ is drawn on the grid.

Write down the coordinates of the turning point of the graph.

Write down the roots of $f(x)=2$

Write down the value of $f(0.5)$

The graph of $y=f(x)$ is drawn on the grid.

Write down the coordinates of the turning point of the graph.

Write down estimates for the roots of $f(x)=0$

Use the graph to find an estimate for $f(1.5)$

Complete the table of values for $y = \frac{1}{x} ( x^{2} + 4 )$

On the grid, draw the graph of $y = \frac{1}{x} ( x^{2} + 4 )$ for 0.25 less-than or slanted equal to x less-than or slanted equal to 8

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 diagram shows part of a sketch of the curve $y=\mathrm{sin}x^{\circ}$

Write down the coordinates of

(i) the point P

(ii) the point Q

Sketch the graph of $y=\mathrm{tan}x$ for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ}$

Show the coordinates of any points of intersection with the coordinate axes.

Complete the table of values for $y=\frac{6}{x}$

On the grid, draw the graph of $y=\frac{6}{x}$ for 0.5 less-than or slanted equal to x less-than or slanted equal to 6

Circle the point that is on the graph of $y=\frac{1}{x}$

The equation of a curve is $y=(x--1)^{2}--6$

Circle the coordinates of the turning point.

The graph of y = x³ − x² − 2 is drawn on the grid.

Use the graph to solve* x*³* − x*² − 2 = 0.

Give your answer correct to 1 decimal place.

*x *= ...................................................

Here is the graph of y = x² + x − 6.

Use the graph to solve the equation x² + x − 6 = 0.

x = ................. or x = ................

(i) Sketch a graph on the axes that shows that y is directly proportional to x.

(ii) Sketch a graph on the axes that shows $y=x^{3}$

Complete the table of values for $y=x^{2}---x---6$

On the grid, draw the graph of $y=x^{2}---x---6$ for values of $x$ from $---3\mathrm{to}3$

Use your graph to find estimates of the solutions to the equation $x^{2}-x-6=---2$

Sketch the graph of $y = \text{cos} x^{ ^{\circ} } \text{for} 0 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360$

The diagram shows part of a sketch of the curve $y=\mathrm{sin}x^{\circ}.$

Write down the coordinates of the point $P$.

Write down the coordinates of the point $Q$.

Complete the table of values for $y=x^{2}-3x+2$

On the grid, draw the graph of $y=x^{2}---3x+2$ for values of $x$ from $---1\mathrm{to}5$

Find estimates for the solutions of the equation $x^{2}-3x+2=4$

Complete the table of values for $y=x^{2}-3x+1$

On the grid, draw the graph of $y=x^{2}---3x+1$ for values of $x$from $---2\mathrm{to}4$

By drawing a suitable straight line on the grid, find estimates for the solutions of

$x^{2}-3x+1=3$

Complete the table of values for $y=x^{2}--5x+6$

On the grid, draw the graph of $y = x ^{2} - 5 x + 6 \text{for} 0 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 5$

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation

$x^{2}--5x=x--7$

Part of the graph of$y=2x^{2}-4x-1$ is shown on the grid.

Use the graph to find estimates for the solutions of the equation $2x^{2}-4x-1=0$

Give your solutions correct to one decimal place.

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation $x^{2}-x-1=0$

Show your working clearly.

Give your solutions correct to one decimal place.

The diagram shows the graph of $y=f(x)$ for $- 4 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 12$

Note: Point P in the graph is from the previous question. It is not required for this question.

The equation $f(x)=k$ has exactly two different solutions for $- 4 \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 12$

Use the graph to find the two possible values of $k$.

Write $3x^{2}-12x+7$ in the form $a(x+b)^{2}+c$

The line $L$ is the line of symmetry of the curve with equation $y=3x^{2}-12x+7$

Using your answer to part (a) or otherwise, write down an equation of $L$.

Circle the point that lies on the curve $y=x^{2}--4x+1$

Here is a sketch of $y=\mathrm{cos}x$for values of $x$ from 0° to 360°

$α^{\circ}$ is an acute angle.

$\mathrm{cos}α^{\circ}=k$

Circle the value of $\mathrm{cos}(180^{\circ}--α^{\circ})$

Circle the value of $\mathrm{cos}\quad (360^{\circ}+α^{\circ})$

Complete the table of values for $y=x^{2}--x--4$

On the grid below, draw the graph of$y=x^{2}--x--4$ for values of $x$ from –3 to 3

Complete the table of values for $y=x^{3}-3x+1$

On the grid, draw the graph of $y=x^{3}-3x+1$ for values of $x$ from − 2 to 2

Here are four graphs.

Write down the letter of the graph that could have the equation $y=-\frac{1}{x^{2}}$

Complete the table of values for $y=x^{2}---2x$

On the grid, draw the graph of $y=x^{2}---2x$for values of $x$ from $---2\mathrm{to}4$

Solve $x^{2}-2x-2=1$

Complete the table of values for $y=x^{2}---2x---1$

On the grid, draw the graph of $y=x^{2}---2x---1$ for values of $x$ from $---2\mathrm{to}4$

Solve $x^{2}-2x-1=x+3$

The diagram shows the graph of $y=x^{2}---4x---2$

Use the graph to find estimates for the solutions of

i) $x^{2}-4x-2=0$

ii) $x^{2}-4x-6=0$

Use the graph to find estimates for the values of $x$ that satisfy the simultaneous equations

$\begin{gathered} y & = x^{2} \text{long} \text{dash} 4 x \text{long} \text{dash} 2 \\ \\ x + y & = 6 \end{gathered}$

Complete the table of values for $y=x^{3}--2x^{2}--3x+4$

On the grid, draw the graph of $y=x^{3}--2x^{2}--3x+4$ for values of $x$ from –2 to 3

By drawing a suitable straight line on the grid, find estimates for the solutions of the equation $x^{3}--2x^{2}--x+1=0$

Give your solutions correct to 1 decimal place.

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

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

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

(ii) the coordinates of the turning point.

Express $7+12x--3x^{2}$ in the form $a+b(x+c)^{2}$ where $a,b$ and$c$are integers.

$C$ is the curve with equation$y=7+12x--3x^{2}$

The point $A$ is the maximum point on $C$

Use your answer to part (a) to write down the coordinates of $A$

Complete the table of values for $y=\frac{1}{2}x^{3}--2x+3$

On the grid, draw the graph of $y = 1 \frac{1}{2} x^{3} - 2 x + 3 \text{for} - 3 less-than \text{or} \text{slanted} \text{equal} \text{to} x less-than \text{or} \text{slanted} \text{equal} \text{to} 3$

By drawing a suitable straight line on the grid, find an estimate for the solution of the equation $\frac{1}{2}x^{3}--x+4=0$

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

The curve $C$ has equation $y=3--5(x+1)^{2}$ The point $A$ is the maximum point on $C$.

Write down the coordinates of $A$.

The curve $C$ has equation $y=x^{2}--6x+4$

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.

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

The point $A$ is the maximum point on $C$.

Write down the coordinates of $A$.

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

The curve $C$ is transformed to the curve $T$.

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

Describe fully the transformation that maps curve $C$ onto curve $T$.

Write $x^{2}+4x-16$ in the form $( x + a )^{2} - b$.

Sketch the graph of $y=x^{2}+4x-16$ , showing clearly the coordinates of any turning points.

Write $x^{2}-10x+22$ in the form $( x - a )^{2} - b$.

Sketch the graph of $y=x^{2}-10x+22$ .

Show clearly the coordinates of any turning points and the value of the $y$-intercept.

The graph of $y=2x^{2}+3x-9$ is drawn below.

Use the graph to solve $2x^{2}+3x-9=0$.

$x=............................\mathrm{or}\,x=............................$

The equation 2x² + x − 4 = 0 can be solved by finding the intersection of the graph of y = 2x² + 3x − 9 and the line y = ax + b.

(i) Find the value of a and the value of* b.*

$\begin{gathered} a = ............................. \\ b = .............................. [ 2 ] \end{gathered}$

(ii) Hence use the graph to solve the equation 2x² + x − 4 = 0.

x = ............................ or *x *= ............................[3]

Sketch the graph of $y = ( x - 2 )^{2} - 3$. Show the coordinates of any turning points.

The sketch shows part of a graph which has equation $y=ax^{2}+bx+c$.

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

$a=.......................................\,b=.......................................\,c=.......................................$

The curve $C$ has equation $y=x^{2}--6x+4$

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.

The diagram shows part of a sketch of the curve $y=\mathrm{sin}x^{\circ}$

Write down the coordinates of (i) the point $P$

(ii) the point $Q$

Sketch the graph of $y=\mathrm{tan}x$for $0 ^{\circ} \text{less} - \text{than} or \text{slanted} \text{equal} to x \text{less} - \text{than} or \text{slanted} \text{equal} to 360 ^{\circ}$

Show the coordinates of any points of intersection with the coordinate axes.

Here are 6 graphs

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

Write your answers on the dotted lines.