Reflections over the X-axis and Y-axis are important changes that impact how we see function graphs. Let’s explain this in simpler terms:

Reflection Over the X-Axis

• What It Means: When we reflect a graph over the X-axis, the new graph shows the opposite values of the original function. This means we take every point on the graph and flip it upside down.

• Example: Take the function $f(x) = x^2$. If we flip this over the X-axis, we get $-f(x) = -x^2$. So, the graph is now upside down!

Reflection Over the Y-Axis

• What It Means: Reflecting a graph over the Y-axis changes the function to use negative values for $x$. This means we replace $x$ with $-x$ in the function.

• Example: For the same function $f(x) = x^2$, reflecting it over the Y-axis gives us $f(-x) = (-x)^2 = x^2$. This shows that the graph stays the same because it is symmetrical. However, for the function $f(x) = x^3$, the reflection over the Y-axis becomes $f(-x) = -x^3$, flipping it to the other side.

Visualizing Reflections

One great way to see these changes is by drawing both the original graph and the reflected graph on the same set of axes. This side-by-side comparison helps us really understand how reflections can change the look and position of the graph. It deepens our awareness of how different functions behave!