Features of a good graph
The graph of a function f should clearly show all the main
characteristics
of the function. These include
-
The domain and range of f
-
How the gaph looks for both positive and negative x values.
-
Intercepts
- Where the function is increasing and where the function is decreasing
-
Maxima and minima (turning points)
-
Concavity (curviness)
- Any symmetry
-
Any asymptotes
-
Any periodicity
-
Any discontinuities (jumps or gaps and points that are not included as
open circles)
The scale and variable name should be indicated clearly on both axes.
The scales on both axes should usually be the same, unless this
distorts
the graph too much. If the variables have physical meaning, label
the axes with that meaning in words and include units.
By looking at your graph, anyone should be able to extrapolate
correctly
how the rest of the graph looks. For example, long term behavior
should be clear and any periodicity should be obvious.
Use graph paper, a straightedge, colored pens, etc. to make the
graph
clear, accurate, and well-drawn.
Do not make the graph too small.
Do not blindly trust your graphing calculator. We will see
that
there are traps one can fall into. Check that the calculator
results are consistent with your mathematical knowledge of the function.