# Algebra/Other Types of Graphs

*22 November 2016*. There are template/file changes awaiting review.

## Sample Graphs of Various Functions and Relations[edit]

y =x y = -x y = |x| y=-|x| y=x^{2}
y=-x^{2} y=x^{3} 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[edit]

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.

which simplifies to degrees * 18 / 5

### Bar Chart[edit]

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.