Graphs are great tools for understanding calculus, especially in Year 9 math. They show ideas that might seem tricky at first, making them easier to grasp.

Key Ideas Explained with Graphs

1. Functions: A graph of a function, like $f(x) = x^2$, helps you see how the output changes when the input changes. This is a good way to start learning about functions in calculus.

2. Limits: Graphs make it easier to understand limits. By watching what happens to $f(x)$ as $x$ gets closer to a certain number, you can get a clear idea of what a limit is. For example, you can see the limit of $f(x)$ as $x$ approaches 2 directly on the graph.

3. Derivatives: The derivative shows how steep a function is at any point. When you look at the tangent line on the graph at a certain point, you can visualize the derivative $f'(x)$. This line shows how steep the graph is right there.

4. Integrals: Finally, graphs help with understanding integrals. The area under the curve of a function from point $a$ to point $b$ represents the integral of that function. This link between area and integration makes things much clearer.

In short, using graphs to visualize these key ideas can really help you understand basic calculus concepts better!