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Graphs of Common Functions 3

Maths: Edexcel A Level Pure Maths, topic 2.5.7

Common Functions

You need to be able to draw the following graphs for your exam. Make sure you know their shapes, intercepts, and behavior at large values.

Square root graph

Square root graph

  • There are no real values for the square root of a negative number, so the square root graph exists only in quadrant I of the Cartesian plane.
  • Only positive values of f(x)f(x) are plotted so that the graph is a function.
  • The reason for this is explained further when we look at functions in more detail.
Cube root graph

Cube root graph

  • The cube root of a negative number gives a negative number, so the graph exists in both quadrants I and III.
Absolute value function

Absolute value function

  • The absolute value function is written as f(x)=∣x∣f(x) = |x|.
  • The function takes each value of xx and gives the magnitude of the value as its output.
  • For example, f(−9)=∣−9∣=9f(-9) = \left|-9\right| = 9
  • The graph exists only in the upper two quadrants of the Cartesian plane.
Piecewise function

Piecewise function

  • A piecewise function is a function that is composed of multiple functions defined on different ranges of xx.
  • The convention for writing the function is shown alongside the graph.
Step function

Step function

  • The step function is a special type of piecewise function.
  • The step function is 0 for negative values of xx and 1 for positive values of xx and for x=0x=0.

Test yourself on Graphs of Common Functions 3

  • Which type of graph is this?

  • Which type of graph has the form y=∣x∣y = |x|?

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