When we talk about how the X and Y axes affect the shape of a graph, there are a few important things to remember, based on my experience in Year 11 Math.

1. How the Graph is Positioned

• X-Axis (Horizontal): The X-axis is usually the bottom line of the graph. It often shows the input values (we can call them $x$). How we set up the X-axis can change what we see in the graph. For example, if we only look at $x$ values from -10 to 10, we might miss important parts of the curve outside that area.

• Y-Axis (Vertical): The Y-axis is the side line of the graph. It usually shows the output values ($f(x)$). By changing the Y-axis scale, we can see small changes in the function that we might miss if the scale is too wide.

2. How the Function Acts

• Where the Graph Crosses the Axes: The points where the graph crosses the X or Y axes are called roots. These points are important because they show where the function equals zero.

• Increasing and Decreasing: Depending on the shape of the graph, the axes can help us see where the function is going up or down.

3. Moving and Flipping the Graph

• Shifting and Reflecting: Moving the graph left or right, or up and down, helps us understand how changing parts of the function affects the results. For example, if we slide the graph down, we change its Y values but keep the X values the same.

In summary, knowing how the X and Y axes work together helps us better understand the function's behavior. This makes it easier for us to analyze and learn from our studies.