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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 = kx) can model population growth, such as monitoring wildlife conservation efforts.

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: Types of Graphs | Mathematics for GCSE/IGCSE - Year 11
    • Quadratic Function: Forms a parabolic curve. Example: Types of Graphs | Mathematics for GCSE/IGCSE - Year 11
    • Cubic Function: Shows a curve with two turning points. Example: Types of Graphs | Mathematics for GCSE/IGCSE - Year 11
    • Reciprocal Function: Reflects over the asymptotes. Example: Types of Graphs | Mathematics for GCSE/IGCSE - Year 11
    • Exponential Function: Shows rapid growth or decay. Example: Types of Graphs | Mathematics for GCSE/IGCSE - Year 11

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

  • You may also need to recognise the shapes of the graphs Types of Graphs | Mathematics for GCSE/IGCSE - Year 11

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

  • 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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Types of Graphs
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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.
The document Types of Graphs | Mathematics for GCSE/IGCSE - Year 11 is a part of the Year 11 Course Mathematics for GCSE/IGCSE.
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