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## 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

$$y=a\sin\theta +q$$

$$y=a\cos\theta +q$$

$$y=a\tan\theta +q$$