Types of Function
Polynomial Function - A function in the form f(x) = Anx n+An-1x n-1+…+ A2x 2+
A1x 1+A0 where A is any real number and n is a whole number.
Constant Function - A polynomial function is called a constant function when
the numerical coefficients of all terms containing variable x is zero.
● It is in the form f(x) = C, where C is a real number.
Linear Function - A polynomial function with degree 1 is called linear
function.
● It is in the form f(x) = mx + b, where m is slope, and b is the y -
intercept.
● The graph of every linear function is always a straight slanting line.
Quadratic Function - A polynomial function of a degree two is a quadratic
function in the form f(x) = ax2 + bx +c, where a, b, and c are real numbers,
and a ≠ 0.
● Quadratic functions are graphically represented by a parabola with
vertex.
Cubic Function - A polynomial function of third degree is a cubic function in
the form f(x) = ax3 + bx2 +cx + d where a, b, c, and d are real numbers, and
where a is not equal to zero.
● Cubic functions are represented by curves passing through (0, 0) with
turning points.
Table of Values - a graphic organizer or chart that helps determine two or
more points that can be used in creating graphs
Operations on Functions
Addition - The sum of two functions 𝑓(𝑥) and 𝑔(𝑥) is denoted by (𝑓+𝑔)(𝑥).
● This sum is defined as (𝑓+𝑔)(𝑥) = 𝑓(𝑥)+𝑔(𝑥).
Subtraction - The difference between the two functions 𝑓(𝑥) and 𝑔(𝑥) is
denoted by (𝑓−𝑔)(𝑥).
● The difference is defined as (𝑓−𝑔)(𝑥) = 𝑓(𝑥)−𝑔(𝑥).
Product - The product of two functions 𝑓(𝑥) and 𝑔(𝑥) is denoted by (𝑓∙𝑔)
(𝑥);
● This product is defined as (𝑓∙𝑔)(𝑥) = 𝑓(𝑥)∙𝑔(𝑥).
Division - the quotient of two functions 𝑓(𝑥)and 𝑔(𝑥) is denoted by ( fg ) ( x );
Polynomial Function - A function in the form f(x) = Anx n+An-1x n-1+…+ A2x 2+
A1x 1+A0 where A is any real number and n is a whole number.
Constant Function - A polynomial function is called a constant function when
the numerical coefficients of all terms containing variable x is zero.
● It is in the form f(x) = C, where C is a real number.
Linear Function - A polynomial function with degree 1 is called linear
function.
● It is in the form f(x) = mx + b, where m is slope, and b is the y -
intercept.
● The graph of every linear function is always a straight slanting line.
Quadratic Function - A polynomial function of a degree two is a quadratic
function in the form f(x) = ax2 + bx +c, where a, b, and c are real numbers,
and a ≠ 0.
● Quadratic functions are graphically represented by a parabola with
vertex.
Cubic Function - A polynomial function of third degree is a cubic function in
the form f(x) = ax3 + bx2 +cx + d where a, b, c, and d are real numbers, and
where a is not equal to zero.
● Cubic functions are represented by curves passing through (0, 0) with
turning points.
Table of Values - a graphic organizer or chart that helps determine two or
more points that can be used in creating graphs
Operations on Functions
Addition - The sum of two functions 𝑓(𝑥) and 𝑔(𝑥) is denoted by (𝑓+𝑔)(𝑥).
● This sum is defined as (𝑓+𝑔)(𝑥) = 𝑓(𝑥)+𝑔(𝑥).
Subtraction - The difference between the two functions 𝑓(𝑥) and 𝑔(𝑥) is
denoted by (𝑓−𝑔)(𝑥).
● The difference is defined as (𝑓−𝑔)(𝑥) = 𝑓(𝑥)−𝑔(𝑥).
Product - The product of two functions 𝑓(𝑥) and 𝑔(𝑥) is denoted by (𝑓∙𝑔)
(𝑥);
● This product is defined as (𝑓∙𝑔)(𝑥) = 𝑓(𝑥)∙𝑔(𝑥).
Division - the quotient of two functions 𝑓(𝑥)and 𝑔(𝑥) is denoted by ( fg ) ( x );
