Function Applications and Graph Analysis
This final page explores practical applications of functions and graph analysis.
The first example involves a function that assigns the greatest common divisor (GCD) of n and 10 to natural numbers n in the set {3, 4, 5, 6, 7, 8}.
Vocabulary: Największy wspólny dzielnik (NWD) means the greatest common divisor.
Students are tasked with:
a) Creating a table of values for this function.
b) Determining the range of the function.
This exercise demonstrates how mathematical concepts like GCD can be represented as functions, bridging abstract math with practical applications.
The second part of the page focuses on analyzing a given function graph, asking students to determine:
a) The function's domain
b) The function's range
c) The function's zeros (roots)
d) Intervals where the function is positive
e) Minimum and maximum values of the function
Highlight: When analyzing a function graph, the domain is read from the x-axis, while the range is read from the y-axis.
This comprehensive graph analysis exercise helps students practice jak odczytać dziedzinę funkcji z wykresu (how to read a function's domain from a graph) and other crucial skills in function interpretation.
Example: In the given graph, the function's zeros occur at x = -5, x = -1, and x = 5, where the graph intersects the x-axis.
These practical exercises reinforce the importance of understanding function concepts for solving real-world problems and interpreting mathematical data.
