Even and Odd Functions

This final page explores the concepts of even and odd functions, which are important in funzioni pari e dispari esercizi svolti PDF (solved exercises on even and odd functions).

Definition:

• An even function satisfies f(-x) = f(x) for all x in its domain.
• An odd function satisfies f(-x) = -f(x) for all x in its domain.

The page provides examples of even, odd, and neither even nor odd functions:

1. y = x² + 3 (even function)
2. y = sin(x) (odd function)
3. y = (x + 3)² (neither even nor odd)

Example: For the function y = 2x³, f(-x) = -2x³, proving it is an odd function.

Highlight: Recognizing even and odd functions can simplify function analysis and graphing, as they exhibit symmetry around the y-axis or origin, respectively.

The page concludes with a brief mention of asymptotes, which are important for understanding the long-term behavior of functions.

Codomain and Axis Intersections

This section focuses on finding the codomain of a function and calculating its intersections with the x and y axes.

Definition: The codomain of a function is the set of all possible output values (y-values) of the function.

The page provides step-by-step instructions for finding intersections with axes:

1. To find x-axis intersections, set y = 0 and solve for x.
2. To find y-axis intersections, set x = 0 and solve for y.

Example: For the function y = (2x - 1) / (7 - x²), the y-axis intersection is at (0, -1/7).

The page also includes graphical representations of functions, illustrating their domains and intersections with axes.

Highlight: Understanding axis intersections is crucial for sketching the graph of a function and analyzing its behavior.