When making graphs of functions, there are some common mistakes that students should watch out for:

1. Wrong Scale: If the scale on the axes isn’t set correctly, it can make the function look different from what it really is. A good rule is to use the same size intervals on both the x-axis and y-axis.

2. Missing Important Points:

   • Intercepts: Always find and plot where the graph crosses the axes. For $x$-intercepts, set $f(x)=0$, and for $y$-intercepts, calculate $f(0)$.
   • Slope and Curvature: Misunderstanding slope, especially in straight-line functions, can change how the graph looks. It's important to see if the slope is going up (positive) or down (negative).

3. Not Using Enough Points: When graphing curves, using just a few points might miss important parts of the function. Try to plot at least 5 to 7 points to show the function's shape accurately.

4. Ignoring Asymptotes and Boundaries: For functions that involve ratios (rational functions), missing vertical and horizontal asymptotes can lead to misleading graphs.

By avoiding these mistakes, students can get much better at graphing functions!