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

• 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.