Visualizando transformaciones de funciones

This is counter-intuitive! It happens because you are changing the "input" value. To get the same output as the parent function at x=0, you now need to input x=-3. Thus, the entire graph shifts 3 units toward the negative side.

For a linear function (like y = mx), yes. For other functions (like x²), a negative sign reflects the entire shape without changing the fundamental growth rate of the variable.

Yes. If you multiply the x *inside* the function, e.g., f(bx), it creates a horizontal dilation. This is less common in standard algebra but very common in trigonometry.

In a parabola, the vertex (h, k) moves exactly according to the shifts. A horizontal shift of +3 moves the vertex to x=3, and a vertical shift of +5 moves it to y=5.

Vertical shifts and reflections directly change the range (y-values). Horizontal shifts change where certain values appear but usually don't change the overall domain of a real-valued polynomial.

Translations and Reflections are "Rigid" because they do not change the size or shape of the graph, only its location. Dilations (stretches) are "Non-Rigid."

The best way is to pick an easy point (like x=0 or the old vertex) and plug it into the new equation to see if the calculated y-value matches your graph.