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      Algebra : Plotting curved graphs

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      • Plotting curved graphs

      Plotting curved graphs

      • Posted by sapayth
      • Categories Algebra, Graphs of non-linear functions
      • Comments 0 comment
      a9-1-plotting-curved-graphs

      Functions

      A function is a rule that maps one number, the input (x) onto an other, the output (y).

      Non-linear functions

      A non-linear function is where the graph displaying the function is curved and therefore not a straight line. An example of a non-linear function is as follows:

      y = x² + 1

      screen-shot-2017-01-15-at-2-44-23-am

      y = 3 + 2³

      Non-linear functions can be plotted as a graph using a graphic calculator or a computer.

      Using a table of values

      The following function is plotted onto a table to help to display on a graph:

      y = x² – 3 (use the values of x between -3 and 3.

      The following are the coordinates of the graph:

      x: -3, -2, -1, 0, 1, 2, 3

      y = x² – 3: 6, 1, -2, -3, 1, 6

      These then provide the following co-ordinates:

      (-3, 6), (-2, 1), (-1, -2), (0, -3), (1, -2), (2, 1), (3, 6)

      These plot then will create the following graph:

      ys-a-9-1-1

      Points to note:

      • The shape of the graph is called a parabola (it is always symmetrical with a minimum or maximum point)
      • This is the characteristic of a quadratic function

      Cubic graph

      ys-a-9-1-2

      The following graph represents a cubic function and represents the following formula:

      y = x³ – 7x +2

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      Graphs of non-linear functions

      • Plotting curved graphs
      • Graphs of important non-linear functions
      • Using graphs to solve equations
      • Solving equations by trial and improvement
      • Function notation
      • Transforming graphs

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