====== Definitions: Mathematics 12: PTB by Muzzammil Subhan======
Definitions from **Calculus and Analytic Geometry, MATHEMATICS 12**, published by Punjab Textbook Board (PTB) Lahore, Pakistan. We are very thankful to [[:people:muzzammil-subhan]] for his valuable contribution. Download or view PDF for all definitions. Samples is given below

=====Sample=====
  * **Polynomial Function:** A function of the form $P(x)=a_0 x^0+a_1 x^1+a_2 x^2+\ldots . .+a_{n-1} x^{n-1}+a_n x^n$ is called polynomial function where $n \in W$ and $a_0, a_1, a_2, \ldots, a_n \in R$.
  * **Linear Function:** A function of the form $f(x)=a x+b$ where $a, b \in R$ and $a \neq 0$ is called linear function.
  * **Identity Function:** A function of the form $f(x)=x$ is called Identity function.
  * **Constant Function:** A function of the form $f(x)=c$ where $c \in R$ is called constant function.
  * **Rational Function:** A function of the form $\frac{P(x)}{Q(x)}$ where $P(x)$ and $Q(x)$ are polynomials and $Q(x) \neq 0$ is called rational function.
  * **Exponential Function:** A function in which variable appear as power of a constant is called exponential Function. E.g. $y=2^x, y=e^x$.
  * **Logarithmic Function:** The functions $f(x)=\log a^x$ and $f(x)=\log e^x$ are called general and natural logarithmic function respectively.
  * **Explicit Function:** If $y$ is easily expressed in term of $x$ then $y$ is called an explicit function. E.g. $y=x^2+3 x, y=\sqrt{x^2+1}$.
  * **Implicit Function:** If $y$ is not expressed in term of $x$ then $y$ is called an implicit function. E.g. $x^2+x y+y^2=4$.
  * **Even Function:** A function $f(x)$ is said to be an even function if $f(-x)=f(x)$.
  * **Odd Function:** A function $f(x)$ is said to be an odd function if $f(-x)=-f(x)$.
  * **Parametric Function:** A function in which x and y are expressed as functions of a third variable is called parametric function.
  * **Inverse Function:** Let $f(x)$ be a bijective function from A to B then its inverse is $f^{-1}(x)$ which is onto function from B to A .
  * **Limit Of A Function:** Let $f(x)$ be a function if the value of $f(x)$ tend to a fixed number " L " as $x$ tends to $a$ then " L " is called limit of $f(x)$ as $x$ tends to $a$. It is written as $\lim f(x)=L$.
  * **Decision Variable:** The variable used in system of linear inequalities relating with the problem are called decision variable.
  * **Feasible Region:** The solution region of an inequality restricted to first quadrant is called feasible region.
  * **Feasible Solution:** Each point of feasible region is called feasible solution of system of linear inequality.
  * **Feasible Solution Set:** Set of all feasible solution of the system of linear inequality is called feasible solution set.
  * **Linear Programming:** Mathematical techniques in which we get maximize or minimize value of variables of linear function is called linear programming.
  * **Nappes:** Two parts of cone are called nappes.
  * **Circle:** “A set of all points in a plane which are equidistant from a fixed point is called circle.” The fixed point is called centre and fixed distance is called radius of circle.
  * **Point Circle:** A circle whose radius is zero is called point circle.
  * **Parabola:** “A set of all points in a plane which are equidistant from fixed point and fixed line.” The fixed point is called focus and fixed line is called directrix of parabola.

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