Transformations of the Reciprocal Function

Key Questions

What is a transformation?

Answer:

An element(point, line, plane or any other geometric, complex or whatever figure) is said to undergo a transformation when ever one or more of its properties are changed.

Explanation:

A transformation just a rule; its more like a function. It takes an object and returns that object's image.

Transformations are done using: functions, matrices, complex numbers etc.

What we call object can be a point, a line etc. The basic fact about all objects is that object haves properties.

For example: The point $A (3, 2)$ $A(3,2)$ has only the property of position(in a Cartesian coordinate system).

Once you change point $A$ $A$ 's position to let's say $B (6, 4)$ $B(6,4)$ by a particular procedure, we say you have transformed point $A$ $A$ to be point $B$ $B$ .

And in which case the object is $A (x, y)$ $A(x,y)$ and the image is $B (6, 4)$ $B(6,4)$

Our transformation could be the matrix: $({:(2" "0),(2" "0):})$

Proof : Because $({:(2" "0),(0" "2):})xx({:(3),(2):})=({:(6),(4):})$

Antoine · 1 · Jul 23 2015
What is the graph of the reciprocal function?

Answer:

The basic reciprocal function is $1/x$

Explanation:

The graph looks like:
graph{1/x [-10, 10, -5, 5]}

MeneerNask · 1 · Jul 19 2015
What is the reciprocal function?

The reciprocal function is:

$f(x)=1/x$

It's graph is as following:

This is an example of asymptote.

Since $x$ can take all values except $0$ for $f(x)$ to be defined,
Domain: $R-{0}$ , i.e., all real numbers except 0.
Range: $R-{0}$ , i.e., all real numbers except 0.

Tanish J. · 1 · Oct 27 2014