Answer to Question #327694 in Functional Analysis for Lee

Question

Represent the rational function f(x)=1/3x-1 using its table values and graph

Answer 1

We present a table for the function $f(x)=\frac{1}{3x}-1$ using $20$ different values of $x$. It is given below:

$\begin{array}{ll} x&f(x)\\ -5&-1.067 \\ -4&-1.083 \\ -3&-1.111 \\ -2&-1.167 \\ -1&-1.333 \\ -0.5&-1.667 \\ -0.4&-1.833 \\ -0.3&-2.111 \\ -0.2&-2.667 \\ -0.1&-4.333 \\ 0.1&2.333 \\ 0.2&0.667 \\ 0.3&0.111 \\ 0.4&-0.167 \\ 0.5&-0.333 \\1&-0.667 \\2&-0.833 \\3&-0.889 \\4&-0.917 \\ 5&-0.933 \\ \end{array}$

The values for $f(x)$ are rounded up to 3 decimal places. The graph of the function is presented below:

It has a vertical asymptote $x=0$ . The horizontal asymptote is: $x=-1$. It is due to the fact that $\frac{1}{3x}\rightarrow0,x\rightarrow\infty$. The function is decaying. It is visible from the derivative: $f'=-\frac{1}{3x^2}$.