Graph the rational function. f(x) = 3/x^2- 2

To sketch the graph of the rational function f(x) = 3/x2 -2, first need to propose values of X. Then evaluate the function to find the corresponding value of y. You need to remember that is a rational function, and you cannot use x = 0, because a division by zero is undefined, it has no meaning.

For the table you should select several negative, and positive numbers, and close to the 0, choose more numbers to have a smooth curve line.

For example:

x = -1

If you substitute in the function [tex]f(x) = \frac{3}{x^2} -2[/tex]

y = f(-1) = 3/(-1)^2-2 = 1

Now for x = 1

y = f(-1) = = 3/(1)^2-2 = 1

Therefore for your chart

x = -1, y = 1 , (-1, 1)

x = 1, y = 1 , (1, 1)

Now you have two points from the graph:

I attached an excel file, there you will see a complete table, with more values for x and y also if you select any value of y, you will see how to do the calculations in each cell from the table. Using excel is helpful to do these type of operations.

Once you have the values in the table, select the data. Then from the bar choose insert and then select the xy scatter. Now you will see your graph.