Algebra/Other Types of Graphs

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Algebra
Algebra
 ← Compound and Absolute Value Inequalities Other Types of Graphs Polynomials → 

Sample Graphs of Various Functions and Relations[edit]

Absolute Value Function.PNG            y = |x|

Function x^2.svg            y = x2

Y=1divided by x.PNG            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.
The same data plotted using a pie chart and a bar chart.

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.

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

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.