Algebraic and transcendental functions

Omar G. Monteagudo, Jun 12, 2015

A book full with applets devoted to understand the behavior of the list of algebraic and transcendental functions that we are going to review this semester.

Table of Contents

  1. Rational functions
    1. Explore Rational Functions
    2. Rational functions sketcher
  2. Inverse functions
    1. The graph of the inverse function
  3. Transformations of a function
    1. Reflections, strechings and compressions
  4. The graph of the exponential function
  5. The graph of the logarithmic function
  6. Conic sections
    1. Ellipses and hyperbolas by means of perpendicular bisectors
    2. Parabola by means of perpendicular bisectors

1.

Rational functions

Rational functions defined by the quotient of degreee one polynomials.

  • 1. Explore Rational Functions
  • 2. Rational functions sketcher

1.1.

Explore Rational Functions

Change the values of a, h, and k to explore rational functions of the form [math]y=a/(x - h) + k.[/math]
Explore Rational Functions
– Samantha Garcia

1.2.

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2.

Inverse functions

This is a set of apps devoted to illustrate the symmetry between the graph of a function and the graph of its inverse. Also helpful to understand the notion behind domain restrictions.

  • 1. The graph of the inverse function

2.1.

The graph of the inverse function

– Omar G. Monteagudo

3.

Transformations of a function

An app devotet to illustrate what happens to a function's graph when its parameters are modified.

  • 1. Reflections, strechings and compressions

3.1.

Reflections, strechings and compressions

– Omar G. Monteagudo

4.

The graph of the exponential function


    This chapter does not contain any resources yet.

5.

The graph of the logarithmic function


    This chapter does not contain any resources yet.

6.

Conic sections

  • 1. Ellipses and hyperbolas by means of perpendicular bisectors
  • 2. Parabola by means of perpendicular bisectors

6.1.

Ellipses and hyperbolas by means of perpendicular bisectors

On a sheet of paper draw a circle and name its center "F_1". Then pick a point and call it F_2. Fold the paper so that F_2 meet the circumference at least 50 times (25 points and their opposite through the diameter): What do you get if the distance between F_1 and F_2 is less than the circle radius? What do you get if the distance between F_1 and F_2 is greater than the circle radius? What do you get if the distance between F_1 and F_2 is equal than the circle radius? By the way, did you notice the relation between the circle radius and the addition or the difference between the highlighted distances?

What do you get if the distance between F_1 and F_2 is less than the circle radius? What do you get if the distance between F_1 and F_2 is greater than the circle radius? What do you get if the distance between F_1 and F_2 is equal than the circle radius? By the way, did you notice the relation between the circle radius and the addition or the difference between the highlighted distances?
– Omar G. Monteagudo

6.2.

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