Algebra/Other Types of Graphs

Sample Graphs of Various Functions and Relations
y = |x|

y = x2

y = 1/x

y =x         y = -x           y = |x|         y=-|x|           y=x2 y=-x2        y=x3         y = 1/x       y=-1/(x-1)

y=x! other functions and relations in other sections

inequalities              parabolas              y=(10 or e) to the x        y = log x

polynomials

cubics and squares

what this means is that the graphs of y = x^N(even) and y = x^N (odd) will always look in certain ways.

Second Graphing section: translations    symmetries     +/- inversions     inverse relations     ellipse    circle     square roots    inequalities of these

Other functions and relations

Symmetry about: x-axis y-axis y=x y=-x

Translation (shift) in x and y directions

stretching about x-axis or y-axis

asymptotes

inverse functions (to be originally introduced in Functions, graphing aspects covered here)

circles

ellipses

inequalities in non-linear relations

stretching relations about x or y axes

Newton's method
 * Given 0=x^a y^b + x^c y^d etc, can deduce asymptotes/intersects from smallest polygon containing points (a,b) (c,d) etc

References:

1. ELEMENTARY GEOMETRY for College Students, 2nd Edition, by Daniel Alexander and
 * Geralyn Koeberlein, Houghton Mifflin Company, Boston, MA 1999.

2. ALGEBRA AND TRIGONOMETRY with Analytic Geometry, Ninth Edition, by Earl Swokowski
 * and Jeffery Cole, Brooks/Cole Publishing Company 1997.



Pie Chart
Pie charts are best used to compare parts to the whole by percentages. By measuring the number of degrees that a piece of the pie chart is, one can find the percentage it represents.

$$\mbox{degrees} = \mbox{percent} \cdot\frac{360}{100}$$

which simplifies to degrees * 18 / 5

Bar Chart
Bar charts are best for plotting the change in something over a period of time. It is nearly the same as a line chart, except that the points are not connected, and instead extend to the bottom of the chart.