Types of Graphs | Mathematics for GCSE/IGCSE - Year 11 PDF Download

Types of Graphs

Why do we need to know what graphs look like?

• Graphs are used in various mathematical contexts but have specific real-world applications.
• For instance, a linear (straight line) graph can represent the route a ship takes to travel between two ports.
• An exponential graph (y = k^x) can model population growth, such as monitoring wildlife conservation efforts.

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What are the shapes of graphs that we need to know?

• Simply recalling facts won't significantly improve your IGCSE Mathematics grade.
• However, being familiar with the general shapes of graphs can help you quickly identify the type of math involved and the features a question may refer to.
• Below are the basic forms of the five types of functions (other than trig graphs) you need to recognize:
  • Linear Function: Represents a straight line. Example:
  • Quadratic Function: Forms a parabolic curve. Example:
  • Cubic Function: Shows a curve with two turning points. Example:
  • Reciprocal Function: Reflects over the asymptotes. Example:
  • Exponential Function: Shows rapid growth or decay. Example:

• You may also need to recognise the shapes of the graphs

• Additionally, you need to recognize the three basic trigonometric graphs. However, these trigonometric graphs are covered in another section.

Drawing Graphs Using a Table

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How to Draw a Graph Using a Table of Values without a Calculator? 

• Before starting, envision how the graph might appear by referring to previous notes on understanding graph shapes.
• Apply the rules of BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction) or the order of operations. Substitute each value into the provided function.
• Plot the points and connect them with a smooth curve.
• If there are any points that seem inconsistent with the overall shape of the curve, revisit your calculations for those points.

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How to Draw a Graph Using a Table of Values with a Calculator? 

• Begin by envisioning how the graph might look based on previous insights into graph shapes.
• Utilize the calculator to substitute values into the function.
• Plot the points and connect them smoothly.
• If any points appear incongruent with the curve's shape, double-check the calculations for accuracy.
• Before you begin, envision the potential appearance of the graph by referencing previous notes on recognizing graph shapes.
• Locate the TABLE function on your CALCULATOR.
• Enter the FUNCTION - f(x)
  (using the ALPHA button and x or X, depending on your calculator's make/model).
  (Press = when you have finished).
  (If you are asked for another function, g(x), just press enter again)
• Enter the Start, End, and Step values (the gap between x values).
• Press = and navigate up and down to view the y values.
• Plot the points and connect them with a smooth curve.
• To prevent errors, enclose negative numbers in brackets and use the (-) key instead of the subtraction key.
• If your calculator lacks a TABLE function, compute each y value individually using the normal calculator mode.