Creating Good Graphs for Math 121
Below we have a number of graphs, and we want you to identify what is needed to
improve them for full credit.
Suppose we want to graph the functions
f ( x)  2 x  3
and
g ( x)  1  3 x  3 x 2  x 3
(Note these equations were created with Microsoft Equation 3.0 to produce good
equations.)
Two Functions
50
0
-6
-4
-2
0
2
4
6
-50
y
Series1
Series2
-100
-150
-200
x
Problems: Too Few Points used, no vertical gridlines, inappropriate label, functions
don’t span the domain
Good Points: Has a title, axes are labeled, used lines for functions
Two Functions
10
0
-4
-2
0
2
4
-10
y
-20
-30
f(x)
-40
g(x)
-50
x
Problems: Too Few Points used, Used curve smoothing option (misses correct function),
functions don’t span the domain, important features of graph missing (point of
intersection)
Good Points: Has a title, axes are labeled, vertical grid applied, good labeling, graph fills
region
Two Functions
50
0
-5
-3
-1
1
3
5
y
-50
-100
-150
g(x)
f(x)
-200
x
Problems: Too Few Points used, Used curve smoothing with points (functions/models
are always lines), functions are mislabeled, important features of graph are hard to see
(domain not adjusted to feature important parts of graph)
Good Points: Has a title, axes are labeled, vertical grid applied, graph fills region, size is
appropriate
Two Functions
20
15
10
f(x)
5
y
g(x)
0
-5
-4
-3
-2
-1
-5
0
1
2
3
-10
-15
-20
x
Problems: Graph area too small, g (x ) does not span the domain
Good Points: Has a title, axes are labeled, vertical grid applied, key points shown, plenty
of points on the curve
Two Functions
35
30
f(x)
25
g(x)
20
15
y
10
5
0
-5
-4
-3
-2
-1
-5 0
1
2
-10
-15
x
Good Graph: This graph would receive full credit showing everything asked for.
Suppose that we have data for the population of a country from 1950 to 2000. We want to
graph the population data and a Malthusian growth model
Population Model
70
60
50
Series1
30
Series2
y
40
20
10
0
0
10
20
30
40
50
60
x
Problems: Graph area too small, model does not span the domain, points used on model
(though could be acceptable for this case with discrete dynamical model), inappropriate
labels for axes and legend
Good Points: Has a title, axes are labeled, vertical grid applied, data appears as points
Population Model
70
Population (P(t))
60
50
40
30
20
Census Data
10
Malthusian Growth
0
0
10
20
30
40
50
60
t (Years after 1950)
Good Graph: Note appropriate title and axis labels, Data as points, Model spanning the
domain, Good size, Sensible legend, all grid lines
Note: The legend is not necessary for this particular graph as it is a single model with a
single data set, so a good title is all that is necessary