When we look at how linear, quadratic, and cubic functions are drawn, it's amazing to see how they change in complexity and behavior.

1. Linear Functions:

• Linear functions are the easiest to understand.
• They look like straight lines, for example, $f(x) = mx + c$.
• These lines have a steady or constant slope, meaning they always rise or fall at the same rate.

2. Quadratic Functions:

• Next, we have quadratic functions, which are shown as $f(x) = ax^2 + bx + c$.
• They create shapes called parabolas, which can open up or down like a U.
• The cool thing about quadratics is that their slope changes depending on the x-values, making them more interesting!

3. Cubic Functions:

• Lastly, there are cubic functions, written as $f(x) = ax^3 + bx^2 + cx + d$.
• These graphs can turn one or two times and stretch forever in both directions.
• They are more complicated because they can go up and down at different points.

Connections:

• All three types of functions have important features: where they cross the axes (intercepts), symmetry in quadratics, and turning points in cubics.
• As we move from linear to cubic, the shapes get more detailed. This shows how each type of function grows in complexity, both mathematically and visually.

So, whether you're marking points on paper or looking at pictures of these functions, you can see how they connect and differ as you move from one to the next on a graph!