Understanding the important parts of a function before you draw its graph is really important for a few reasons:

1. Intercepts:

   • The $x$-intercept is the point where the graph crosses the $x$-axis. This happens when $f(x)=0$.
   • The $y$-intercept is where the graph crosses the $y$-axis. This occurs when $x=0$.

2. Slope:

   • The slope shows how steep the line is and in which direction it goes. For a straight-line function like $f(x)=mx+b$, the slope, represented by $m$, tells us whether the line goes up or down and how steep it is.

3. Critical Points:

   • Finding the highest (maximum) or lowest (minimum) points helps us to see the overall shape of the graph.

When you understand these features, it makes it easier to draw the graph correctly and understand how the function behaves.