Syllabus Edition
First teaching 2021
Last exams 2024
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Types of Graphs (CIE IGCSE Maths: Extended)
Revision Note
Author
Daniel IExpertise
Maths
Types of Graphs
Why do we need to know what graphs look like?
- Graphs are used in various aspects of mathematics – but in the real world they can take on specific meanings
- For example a linear (straight line) graph could be the path a ship needs to sail along to get from one port to another
- An exponential graph () can be used to model population growth – for instance to monitor wildlife conservation projects
What are the shapes of graphs that we need to know?
- Recalling facts alone won’t do much for boosting your IGCSE Mathematics grade!
- But being familiar with the general shapes of graphs will help you quickly recognise the sort of maths you are dealing with and features of the graph a question may refer to
- Below the basic form of the five types of function (other than trig graphs) you need to recognise;
- linear ()
- quadratic ()
- cubic ()
- reciprocal ()
- exponential ()
- In addition, you need to recognise the three basic trigonometric graphs- but these are dealt with in another section
Worked example
Match the graphs to the equations.
Graphs:
A
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B
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C
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D
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E
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Equations:
(1) , (2) , (3) , (4) , (5)
Starting with the equations,
(1) is a linear equation (y = mx + c) so matches the only straight line, graph (D)
(2) is an exponential equation with a positive coefficient so matches graph (A)
(3) is a cubic equation with a negative coefficient so matches graph (E)
(4) is a reciprocal equation (notice that it takes the same form as inverse proportion) with a positive coefficient so matches graph (B)
(5) is a quadratic equation with a negative coefficient so matches graph (C)
Graph (A) → Equation (2)
Graph (B) → Equation (4)
Graph (C) → Equation (5)
Graph (D) → Equation (1)
Graph (E) → Equation (3)
Drawing Graphs Using a Table
How do we draw a graph using a table of values without using a calculator?
- Before you start, think what the graph might look like- see the previous notes on being familiar with shapes of graphs
- Using the rules of BIDMAS/ order of operations, substitute each - value into the given function
- PLOT POINTS and join with a SMOOTH CURVE
- If there are any points that don't seem to fit with the shape of the rest of the curve, check your calculations for them again!
How do we draw a graph using a table of values with a calculator?
- Before you start, think what the graph might look like – see the previous notes on being familiar with shapes of graphs
- Find the TABLE function on your CALCULATOR
- Enter the FUNCTION – f(x)
(use ALPHA button and x or X, depending on make/model)
(Press = when finished)
(If you are asked for another function, g(x), just press enter again) - Enter Start, End and Step (gap between x values)
- Press = and scroll up and down to see y values
- PLOT POINTS and join with a SMOOTH CURVE
- To avoid errors always put negative numbers in brackets and use the (-) key rather than the subtraction key
- If your calculator does not have a TABLE function, then you will have to work out each y value separately using the normal mode on your calculator
Exam Tip
- When using the TABLE function of your calculator, double-check that your calculator's y-values are the same as any that are given in the question
Worked example
Calculator Allowed
(a)
Complete the table of values for the function .
Use the TABLE function on your calculator for , starting at -3, ending at 3 and with steps of 1
If your calculator does not have a TABLE function then substitute the values of into the function one by one for the missing values, being careful to put negative numbers in brackets, e.g.
(b)
On the grid provided, draw the graph of for values of from to .
Carefully plot the points from your table of values in (a) on the grid, noting the different scales on the and axes
For example, the first column represents the point
After plotting the points, join them with a smooth curve- do not use a ruler!
It is best practice to label the curve with its equation
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