Name: Graph of Rational Functions
Uploaded: 2019-07-19
Duration: 54 min 4 s
Description: In this video, we will learn the concept of graphing the rational functions and the number of asymptotes in that graph in detail, using various examples.

Question

On your GDC, graph each function and its inverse on the same grid.

$y = \frac{3}{x} - 1$

Accepted Answer

The graph of the inverse of a function reflects two things, one is the function and second is the inverse of the function, over the line $y = \frac{3}{x} - 1$ . This line in the graph passes through the origin and has slope value $1$ . It can be represented as;

$y = f^{- 1} (x)$

which is equal to;

$x = f (y)$

This relation is somewhat similar to $y = f (x)$ , which defines the graph of $f$ but the part of $x$ and $y$ are reversed here. So if we have to draw the graph of $f^{- 1}$ , then we have to switch the positions of $x$ and $y$ in axes.

Generally, the method of calculating an inverse is swapping of coordinates $x$ and $y$ . This newly created inverse is a relation but not necessarily a function.

The original function has to be a one-to-one function to assure that its inverse will also be a function. A function is said to be a one-to-one function only if every second element corresponds to the first value (values of $x$ and $y$ are used only once).

Here we have to draw it using GDC. We will put the equation in calculator we will get the graph of the function $y = \frac{3}{x} - 1$ and its inverse function is $f^{- 1} (x) = \frac{3}{x + 1}$ .

On your GDC, graph each function and its inverse on the same grid.

$y = \frac{3}{x} - 1$

Important Questions on Graphs of Rational Functions

Learn and Prepare for any exam you want !

On your GDC, graph each function and its inverse on the same grid. y=3x-1

Important Questions on Graphs of Rational Functions

Learn and Prepare for any exam you want !

On your GDC, graph each function and its inverse on the same grid.

$y = \frac{3}{x} - 1$