MATEMATICA — Esercizio 08

📋 Testo

Rational function study: draw y = 1/x using the graph.

Carefully observe the behaviour:
- What happens as x approaches 0 from the right? And from the left?
- Is the function defined at x = 0? Why?
- What happens for very large values of x (x → +∞)?
- Is the graph symmetric? With respect to what?

Zoom in on the area near x = 0 to better observe the behaviour.

Analisi: This exercise introduces asymptotes. Ask: 'What do you notice near x ≈ 0? Does the graph seem to approach something without ever touching it?' Guide toward the concept of a vertical asymptote (x = 0) and horizontal asymptote (y = 0). Ask what 'origin symmetry' means (odd function).