Answer to Question #327694 in Functional Analysis for Lee

Question #327694
Represent the rational function f(x)=1/3x-1 using its table values and graph
1
Expert's answer
2022-04-13T13:48:39-0400

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}\nx&f(x)\\\\\n-5&-1.067\n\\\\\n-4&-1.083\n\\\\\n-3&-1.111\n\\\\\n-2&-1.167\n\\\\\n-1&-1.333\n\\\\\n-0.5&-1.667\n\\\\\n-0.4&-1.833\n\\\\\n-0.3&-2.111\n\\\\\n-0.2&-2.667\n\\\\\n-0.1&-4.333\n\\\\\n0.1&2.333\n\\\\\n0.2&0.667\n\\\\\n0.3&0.111\n\\\\\n0.4&-0.167\n\\\\\n0.5&-0.333\n\\\\1&-0.667\n\\\\2&-0.833\n\\\\3&-0.889\n\\\\4&-0.917\n\\\\\n5&-0.933\n\\\\\n\n\\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}".



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