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6.8 Chapter summary (EMA5K)

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  • 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

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

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

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