6.8 Chapter summary

6.8 Chapter summary (EMA5K)

Presentation: 2G2K

• Characteristics of functions:

  • The given \(x\)-value is known as the independent variable, because its value can be chosen freely. The calculated \(y\)-value is known as the dependent variable, because its value depends on the \(x\)-value.

  • The domain of a function is the set of all \(x\)-values for which there exists at most one \(y\)-value according to that function. The range is the set of all \(y\)-values, which can be obtained using at least one \(x\)-value.

  • An asymptote is a straight line, which the graph of a function will approach, but never touch.

• Special functions and their properties:

  • Linear functions of the form \(y=ax+q\).

  • Parabolic functions of the form \(y=a{x}^{2}+q\).

  • Hyperbolic functions of the form \(y=\frac{a}{x}+q\).

  • Exponential functions of the form \(y=a{b}^{x}+q\).

  • Trigonometric functions of the form

    \(y=a\sin\theta +q\)

    \(y=a\cos\theta +q\)

    \(y=a\tan\theta +q\)