When you look at function graphs, there are some important things to notice. Here’s an easy guide based on what I've learned:

1. Intercepts:

   • X-intercepts: These are the spots where the graph crosses the x-axis. You can find them by solving the equation $f(x)=0$.
   • Y-intercept: This is where the graph crosses the y-axis. You can find it by checking $f(0)$.

2. Asymptotes:

   • Vertical Asymptotes: These lines show where the function goes off to infinity. You usually find them by looking for values that make the bottom part of a fraction zero, if the function is a fraction.
   • Horizontal Asymptotes: These show what happens to the graph when $x$ gets really big or really small. They tell you what value the function gets closer to at the ends.

3. Behavior at Infinity:

   • It’s helpful to see what the function does as $x$ goes to really big numbers or really small numbers. Figuring out if it’s going up or down, and what it gets close to, helps you understand the overall shape of the graph.

4. End Behavior:

   • Don’t forget to think about the leading coefficient and the degree of polynomial functions! They can tell you if the ends of the graph go up or down.

By keeping these points in mind, you'll better understand the function's graph and make smarter conclusions about how it behaves. Happy graphing!