- Function is a relation between given set of elements, domain and codomain, which associates each element of domain with only one codomain. The elements can be anything such as words, objects or qualities but they are usually mathematical quantities. Analysis is the area of mathematics where function is taken as a primary object.
2) How was it found?
- The idea of function started to develop in 17 century. Rene Descartes, a philosopher, used the concept to describe various mathematical relationships in his book ‘Geometry’. The name “FUNCTION” was made by Gottfried Wilhelm Leibniz, also a philosopher. Lastly, idea of function was formalized when Leonhard Euler, a mathematician, introduced y=f(x) which is the notation.
3) Types of Functions
A. Linear function
- Generalized Form : f(x) = ax+b (a≠0)
- Linear function is a first-degree polynomial function of one variable.
- Their graph in coordinate plane is a straight line and usually written in slope-intercept form.
- Graph
B. Quadratic function
- Generalized Form : f(x) = ax2+bx+c (a≠0)
- Quadratic function has a graph of parabola that has major axis parallel to y-axis.
- The solution of this function is usually called the root of the equation.
- Graph
C. Cubic function
- Generalized Form : ax3+bx2+cx+d (a≠0)
- The derivative and intergral of cubic function is called quadratic function.
- Solving cubic equation = finding roots of cubic function
- Graph
D. Monotonic function
- Monotonic function tends to move in only one direction as the x value increases.
- It preserves the given order and you learn this term in calculus.
- Graph
E. Periodic function
- Periodic function repeats the value in regular periods.
- ex) trigonometric functions, oscillations, waves etc.
-
1) What is a function?
- Function is a relation between given set of elements, domain and codomain, which associates each element of domain with only one codomain. The elements can be anything such as words, objects or qualities but they are usually mathematical quantities. Analysis is the area of mathematics where function is taken as a primary object.2) How was it found?
- The idea of function started to develop in 17 century. Rene Descartes, a philosopher, used the concept to describe various mathematical relationships in his book ‘Geometry’. The name “FUNCTION” was made by Gottfried Wilhelm Leibniz, also a philosopher. Lastly, idea of function was formalized when Leonhard Euler, a mathematician, introduced y=f(x) which is the notation.3) Types of Functions
A. Linear function
- Generalized Form : f(x) = ax+b (a≠0)- Linear function is a first-degree polynomial function of one variable.
- Their graph in coordinate plane is a straight line and usually written in slope-intercept form.
- Graph
B. Quadratic function
- Generalized Form : f(x) = ax2+bx+c (a≠0)- Quadratic function has a graph of parabola that has major axis parallel to y-axis.
- The solution of this function is usually called the root of the equation.
- Graph
C. Cubic function
- Generalized Form : ax3+bx2+cx+d (a≠0)- The derivative and intergral of cubic function is called quadratic function.
- Solving cubic equation = finding roots of cubic function
- Graph
D. Monotonic function
- Monotonic function tends to move in only one direction as the x value increases.- It preserves the given order and you learn this term in calculus.
- Graph
E. Periodic function
- Periodic function repeats the value in regular periods.- ex) trigonometric functions, oscillations, waves etc.
-
- Graph
4) Educational Videos to Watch
A. What is a function?
B. Cubic function
6) Work Cited
"Cubic function - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 17 Jan. 2010. <http://en.wikipedia.org/wiki/Cubic_function>." Function - History Of Functions ." Science Encyclopedia. N.p., n.d. Web. 17 Jan. 2010. <http://science.jrank.org/pages/2881/Function-History-functions.html>.
"Linear function - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 17 Jan. 2010. <http://en.wikipedia.org/wiki/Linear_function>.
"Monotonic function - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 17 Jan. 2010. <http://en.wikipedia.org/wiki/Monotonic_function>.
"Periodic function - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 17 Jan. 2010. <http://en.wikipedia.org/wiki/Periodic_function>.
"Quadratic function - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia. N.p., n.d. Web. 17 Jan. 2010. <http://en.wikipedia.org/wiki/Quadratic_function>.
"Types of Functions." Oracle ThinkQuest Library . N.p., n.d. Web. 17 Jan. 2010. <http://library.thinkquest.org/2647/algebra/functype.htm>.
" YouTube - Graphing Cubic Functions ." YouTube - Broadcast Yourself. . N.p., n.d. Web. 17 Jan. 2010. <http://www.youtube.com/watch?v=pFUrhIaK8XM>.
" YouTube - Graphing Linear Functions by Finding X,Y Intercept ." YouTube - Broadcast Yourself. . N.p., n.d. Web. 17 Jan. 2010. <http://www.youtube.com/watch?v=mxBoni8N70Y>.