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Which Relation Is Not a Function? Explanation and Examples

In mathematics, you will come across relations and functions quite often, but one burning question that arises in many students’ minds is which relation is not a function. A relation that does not have the properties of a function is just a simple relation. Every function is a relation but every relation is not a […]

Reflection Function – Explanation and Examples

A reflection of a function is a type of transformation of the graph of a function. The reflection of a function can be over the x-axis or y-axis, or even both axes. For example, the reflection of the function $y = f(x)$ can be written as $y = – f(x)$ or $y = f(-x)$ or […]

Extreme Value Theorem – Explanation and Examples

The extreme value theorem states that a function has both a maximum and a minimum value in a closed interval $[a,b]$ if it is continuous in $[a,b]$. We are interested in finding the maxima and the minima of a function in many applications. For example, a function describes the oscillation behavior of an object; it […]

Implicit Function Theorem – Explanation and Examples

In mathematics, more importantly in multivariable calculus, the implicit function theorem is used to solve polynomial equations that cannot be expressed as a function. We state it for a two-variable relation as follows: Let $f(x,y)$ is a relation with $f(x_0, y_0) = c$ and $f’_y(x_0, y_0) neq 0$; then around $(x_0, y_0)$ there exists a […]

Applied Calculus: Comprehensive Definition and Detailed Examples

“Applied Calculus” is a single-level course that covers the basics of several topics such as functions, derivatives and integrals. It is also known as “baby calculus” and discusses several topics which are also part of a calculus course. In this topic, we will discuss applied calculus, its similarities and differences with calculus, and its related […]