2.5.7

Graphs of Common Functions 3

Test yourself

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.

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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.
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Cube root graph

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

  • The absolute value function is written as f(x)=xf(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.
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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.
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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.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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