Page 1: Odczytywanie Własności Funkcji z Wykresu

This page presents a comprehensive example of odczytywanie własności funkcji z wykresu zadania (exercises on reading function properties from a graph). The graph shown is of a piecewise function, and various properties are identified and described.

Vocabulary: Piecewise function - a function defined by different expressions on different intervals of its domain.

The domain of the function is identified as x ∈ $-7, 8$, indicating the function is defined for all x values between and including -7 and 8. This is an essential aspect of odczytywanie własności funkcji z wykresu klasa 1 liceum (reading function properties from a graph for 1st year high school).

Definition: Domain - the set of all possible input values (x-values) for which the function is defined.

The range of the function is given as y ∈ $-1, 3$, showing the set of all possible output values. This demonstrates a key aspect of jak odczytać zbiór wartości funkcji (how to read the range of a function).

Highlight: The range is a crucial property in understanding the behavior of a function and is often a focus in odczytywanie własności funkcji z wykresu zadania maturalne (matura exam tasks on reading function properties from graphs).

The monotonicity of the function is described for different intervals, showcasing jak określić monotoniczność funkcji (how to determine the monotonicity of a function). The function is increasing on $-7, -4$ and [0, 3], decreasing on $-4, 0$ and [7, 8], and constant on [3, 7].

Example: For instance, the function is increasing on the interval $-7, -4$, meaning as x increases from -7 to -4, y also increases.

The zero of the function is identified at x = 2, which is a key point in odczytywanie własności funkcji kwadratowej z wykresu (reading properties of quadratic functions from graphs), although this particular function is not quadratic.

Definition: Zero of a function - a point where the function's value equals zero, i.e., where the graph crosses the x-axis.

Lastly, the extreme values are noted. The maximum value is y = 3, occurring at x = -7, and the minimum value is y = -1, occurring for all x in the interval [3, 7]. This illustrates an important aspect of zbiór wartości funkcji (range of a function) analysis.

Highlight: The presence of a constant section where the function attains its minimum value over an interval is a noteworthy feature, often explored in monotoniczność funkcji zadania (monotonicity of functions exercises).