Graphing functions in pre-calculus can be tough for many students. Here are some challenges you might face:

1. Understanding How Functions Work: Functions can act in different ways, and figuring that out can be hard. It can be confusing to spot things like intercepts, especially with complicated equations.

2. Finding Intercepts: You need to know where a graph crosses the axes. This includes both the $x$ and $y$ intercepts. Finding these points often means solving equations, which can take a lot of time and requires solid algebra skills.

3. Calculating Slope: For straight-line functions, knowing how to find the slope can be tricky. You use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. This can be frustrating, especially if fractions and negative numbers are challenging for you.

4. Curvature and Non-linear Functions: As you study more complex shapes, like parabolas and other curves, it can be tough to understand how they bend. Distinguishing between "concave up" and "concave down" isn’t always easy.

Even with these challenges, there are good ways to get better at graphing:

• Practice: Drawing graphs regularly can help you understand how different functions work.

• Use Technology: Graphing calculators and software can show you visuals. This way, you can double-check your work and see if you understand correctly.

• Break Down Problems: Focus on one thing at a time, like finding the intercepts first before moving on to slopes or curvy shapes.

With practice and the right tools, dealing with graphing functions can go from being frustrating to something you can handle. Start slowly and build your confidence step by step!