# 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 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.