Graphs are a great way to see how functions work and change. When we draw functions on a graph, we're not just placing dots. We're telling a story about how these functions behave with different numbers. Here are some things we can learn from graphs:

1. Slope and Rate of Change: The slope shows us how steep a line or curve is. If the graph is going up quickly, it means the values are increasing fast. This is helpful for spotting trends.

2. Intercepts: The places where the graph crosses the x-axis and y-axis are important. The x-intercepts show where the function equals zero, and the y-intercept shows what the function's value is when $x$ is zero. These points help us understand how the function behaves over time.

3. Behavior at Extremes: Looking at how a graph acts when $x$ gets very big or very small can tell us about the function's limits. For instance, if the graph levels off as $x$ increases, we know the function is staying close to a certain value.

4. Symmetry: Some functions have symmetry, which can make them easier to graph. If a function is even, like $f(x) = x^2$, it looks the same on both sides of the line. Odd functions, like $f(x) = x^3$, have a different kind of symmetry around a central point.

5. Turning Points: Graphs can have high points (maxima) and low points (minima). These turning points show when the function changes direction, which is important in finding the best solutions to problems.

6. Intervals of Increase/Decrease: By looking at parts of the graph, we can see where the function is going up or down. This helps us understand the general trend of the function.

In summary, drawing graphs not only helps us visualize functions but also lets us discover important information about how they behave. With practice, you'll get better at reading these graphs and understanding the stories they tell!